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  • 1.
    Aiki, Toyohiko
    et al.
    Tokyo Womens University.
    Muntean, Adrian
    Netherlands.
    Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 93, p. 3-14Article in journal (Refereed)
    Abstract [en]

    We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.

  • 2.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    A quasistatic frictional problem with normal compliance penalization term1999In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 37, p. 689-705Article in journal (Refereed)
  • 3.
    Argaez, C.
    et al.
    Dublin Institute of Technology.
    Melgaard, M.
    Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry2012In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 75, no 1, p. 384-404Article in journal (Refereed)
    Abstract [en]

    We establish the existence of infinitely many distinct solutions to the multi-configurative Hartree-Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy root-alpha(-2)Delta(xn) + alpha(-4) - alpha(-2) for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Z(tot) of K nuclei is greater than N - 1 and that Z(tot) is smaller than a critical charge Z(c). The proofs are based on a new application of the Lions-Fang-Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert-Riemann manifold, in combination with density operator techniques. (C) 2011 Elsevier Ltd. All rights reserved.

  • 4.
    Argaez, C.
    et al.
    Dublin Institute of Technology.
    Melgaard, M.
    Dublin Institute of Technology.
    Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry (vol 75, pg 384, 2012)2012In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 75, no 6, p. 3274-3275Article in journal (Refereed)
  • 5.
    Arnarson, Teitur
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Poghosyan, Michael
    Yerevan State Univ, Dept Math & Mech.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A PDE approach to regularity of solutions to finite horizon optimal switching problems2009In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 12, p. 6054-6067Article in journal (Refereed)
    Abstract [en]

    We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C-l,C-l-regular away for the free boundaries of the action sets.

  • 6.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 134, p. 70-104Article in journal (Refereed)
    Abstract [en]

    We develop a framework for studying variational problems in Banach spaces with respect to gradient relations, which encompasses many of the notions of generalized gradients that appear in the literature. We stress the fact that our approach is not dependent on function spaces and therefore applies equally well to functions on metric spaces as to operator algebras. In particular, we consider analogues of Dirichlet and obstacle problems, as well as first eigenvalue problems, and formulate conditions for the existence of solutions and their uniqueness. Moreover, we investigate to what extent a lattice structure may be introduced on ( ordered) Banach spaces via a norm-minimizing variational problem. A multitude of examples is provided to illustrate the versatility of our approach. (C) 2015 Elsevier Ltd. All rights reserved.

  • 7. Avelin, Benny
    et al.
    Lundström, Niklas L.P
    Nyström, Kaj
    Optimal doubling, Reifenberg flatness and operators of p-Laplace type2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 17, p. 5943-5955Article in journal (Refereed)
    Abstract [en]

    In this paper we consider operators of p-Laplace type of the form ∇·A(x,∇u) = 0. ConcerningA we assume, for p ∈ (1,∞) fixed, an appropriate ellipticity type condition, H¨older continuityin x and that A(x, ) = ||p−1A(x, /||) whenever x ∈ Rn and ∈ Rn \ {0}. Let  ⊂ Rn be abounded domain, let D be a compact subset of . We say that ˆu = ˆup,D, is the A-capacitaryfunction for D in  if ˆu ≡ 1 on D, ˆu ≡ 0 on @ in the sense of W1,p0 () and ∇·A(x,∇ˆu) = 0 in \D in the weak sense. We extend ˆu to Rn \  by putting ˆu ≡ 0 on Rn \ . Then there existsa unique finite positive Borel measure ˆμ on Rn, with support in @, such thatZ hA(x,∇ˆu),∇i dx = −Z dˆμ whenever ∈ C∞0 (Rn \ D).In this paper we prove that if  is Reifenberg flat with vanishing constant, thenlimr→0infw∈∂ˆμ(B(w, r))ˆμ(B(w, r))= limr→0supw∈∂ˆμ(B(w, r))ˆμ(B(w, r))= n−1,for every , 0 < ≤ 1. In particular, we prove that ˆμ is an asymptotically optimal doublingmeasure on @.

  • 8.
    Avelin, Benny
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Optimal doubling, reifenberg flatness and operators of p-laplace type2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 17, p. 5943-5955Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider equations of p-Laplace type of the form A(x,u)=0. Concerning A we assume, for p∈(1,) fixed, an appropriate ellipticity type condition, Hölder continuity in x and that A(x,η)=|η|p−1A(x,η/|η|) whenever xRn and ηRn∖{0}. Let ΩRn be a bounded domain, let D be a compact subset of Ω. We say that is the A-capacitary function for D in Ω if on D, on Ω in the sense of and in ΩD in the weak sense. We extend to RnΩ by putting on RnΩ. Then there exists a unique finite positive Borel measure on Rn, with support in Ω, such that In this paper, we prove that if Ω is Reifenberg flat with vanishing constant, then for every τ, 0<τ≤1. In particular, we prove that is an asymptotically optimal doubling measure on Ω.

  • 9.
    Avelin, Benny
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Nyström, Kaj
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Wolff-Potential Estimates and Doubling of Subelliptic p-harmonic measures2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 85, p. 149-159Article in journal (Refereed)
    Abstract [en]

    Let be a system of C vector fields in Rn satisfying Hörmander’s finite rank condition and let Ω be a non-tangentially accessible domain with respect to the Carnot–Carathéodory distance d induced by X. We prove the doubling property of certain boundary measures associated to non-negative solutions, which vanish on a portion of Ω, to the equation

    Given p, 1<p<, fixed, we impose conditions on the function A=(A1,…,Am):Rn×RmRm, which imply that the equation is a quasi-linear partial differential equation of p-Laplace type structured on vector fields satisfying the classical Hörmander condition. In the case p=2 and for linear equations, our result coincides with the doubling property of associated elliptic measures. To prove our result we establish, and this is of independent interest, a Wolff potential estimate for subelliptic equations of p-Laplace type.

  • 10. Babaoglu, Ceni
    et al.
    Bazarganzadeh, Mahmoudreza
    Stockholm University, Faculty of Science, Department of Mathematics.
    Some properties of two-phase quadrature domains2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 10, p. 3386-3396Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate general properties of the two-phase quadrature domain, which was recently introduced by Emamizadeh, Prajapat and Shahgholian. The concept, which is a generalization of the well-known one-phase domain, introduces substantial difficulties with interesting features even richer than those of the one-phase counterpart. For given positive constants lambda(+/-) and two bounded and compactly supported measures mu(+/-), we investigate the uniqueness of the solution of the following free boundary problem: {Delta u =(lambda(+)chi(Omega)+ - mu(+)) - (lambda(-)chi(Omega)- - mu(-)), in R(N)(N >= 2), u = 0, in R(N)\Omega, (1) where Omega = Omega(+) boolean OR Omega(-). It is further required that the supports of mu(+/-) should be inside Omega(+/-); this in general may fail and give rise to non-existence of solutions. Along the paths to various properties that we state and prove here, we also present several conjectures and open problems that we believe should be true.

  • 11. Babaoglu, Ceni
    et al.
    Bazarganzadeh, Mahmoudreza
    Department of Mathematics, Stockholm University.
    Some properties of two-phase quadrature domains2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 10, p. 3386-3396Article in journal (Refereed)
  • 12.
    Baroni, Paolo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Lorentz estimates for obstacle parabolic problems2014In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 96, p. 167-188Article in journal (Refereed)
    Abstract [en]

    We prove that the spatial gradient of (variational) solutions to parabolic obstacle problems of p-Laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of Lorentz spaces. 

  • 13.
    Baroni, Paolo
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Colombo, Maria
    Mingione, Giuseppe
    Harnack inequalities for double phase functionals2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 121, p. 206-222Article in journal (Refereed)
    Abstract [en]

    We prove a Harnack inequality for minimisers of a class of non-autonomous functionals with non-standard growth conditions. They are characterised by the fact that their energy density switches between two types of different degenerate phases.

  • 14.
    Bartoszek, Krzysztof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Pulka, Malgorzta
    Gdansk University of Technology.
    Asymptotic properties of quadratic stochastic operators acting on the L1 space2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, p. 26-39Article in journal (Refereed)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.

  • 15.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pulka, Malgorzta
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    Asymptotic properties of quadratic stochastic operators acting on the L1 space2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, p. 26-39Article in journal (Refereed)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.

  • 16.
    Basarab-Horwath, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Lahno, V.
    Zhdanov, R.
    Classifying evolution equations2001In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 47, no 8, p. 5135-5144Article in journal (Refereed)
    Abstract [en]

    A Lie point symmetry classification of evolution equations in 1+1 time-space dimensions was presented. A combination of the standard Lie algorithm for point symmetry and the equivalence group of the given type of equation was used for the classification. For each canonical evolution the maximal symmetry algebra was calculated and related theorems were proved.

  • 17.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Korte, Riikka
    Aalto University, Finland.
    Minima of quasisuperminimizers2017In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 155, p. 264-284Article in journal (Refereed)
    Abstract [en]

    We show that, unlike minima of superharmonic functions which are again superharmonic, the same property fails for Q-quasisuperminimizers. More precisely, if u(i) is a Q(i)-quasisuperminimizer, i = 1,2, where 1 amp;lt; Q(1) amp;lt; Q(2), then u = min{u(1), u(2)} is a Q-quasisuperminimizer, but there is an increase in the optimal quasisuperminimizing constant Q. We provide the first examples of this phenomenon, i.e. that Q amp;gt; Q(2). In addition to lower bounds for the optimal quasisuperminimizing constant of u we also improve upon the earlier upper bounds due to Kinnunen and Martio. Moreover, our lower and upper bounds turn out to be quite close. We also study a similar phenomenon in pasting lemmas for quasisuperminimizers, where Q = Q(1)Q(2) turns out to be optimal, and provide results on exact quasiminimizing constants of piecewise linear functions on the real line, which can serve as approximations of more general quasiminimizers. (C) 2017 Elsevier Ltd. All rights reserved.

  • 18.
    Björn, Anders
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mäkäläinen, Tero
    University of Jyväskylä.
    Parviainen, Mikko
    Helsinki University of Technology.
    Nonlinear balayage on metric spaces2009In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 5-6, p. 2153-2171Article in journal (Refereed)
    Abstract [en]

    We develop a theory of balayage on complete doubling metric measure spaces supporting a Poincaré inequality. In particular, we are interested in continuity and p-harmonicity of the balayage. We also study connections to the obstacle problem. As applications, we characterize regular boundary points and polar sets in terms of balayage.

  • 19.
    Cheng, Yuanji
    Luleå tekniska universitet.
    On the existence of radial solutions of a nonlinear elliptic equation on the unit ball1995In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 24, no 3, p. 287-307Article in journal (Refereed)
  • 20.
    Cianchi, Andrea
    et al.
    University of Firenze, Italy.
    Mazya, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. RUDN University, Russia.
    Quasilincar elliptic problems with general growth and merely integrable, or measure, data2017In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 164, p. 189-215Article in journal (Refereed)
    Abstract [en]

    Boundary value problems for a class of quasilinear elliptic equations, with an Orlicz type growth and L-1 right-hand side are considered. Both Dirichlet and Neumann problems are contemplated. Existence and uniqueness of generalized solutions, as well as their regularity, are established. The case of measure right-hand sides is also analyzed. (C) 2017 Published by Elsevier Ltd.

  • 21.
    Dechevsky, Lubomir
    Luleå tekniska universitet.
    Integral representation of local and global diffeomorphisms2003In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 4, no 2, p. 203-221Article in journal (Refereed)
    Abstract [en]

    The identification of a smooth invertible map between two closed domains in ℝn is of great importance in neuroimaging and other fields where the domains of images must be nonlinearly transformed so as to align important features. The theory for locally diffeomorphic maps is classic, but much less is known about global diffeomorphisms between closed simply connected sets. These bijectively map interiors onto interiors and boundaries onto boundaries. We use this property and the integral of the exponential map to construct representations of global diffeomorphisms for star-shaped domains. As a simple example, details are provided for maps in two dimensions. Applications are outlined for three types of inverse problems related to image registration, diffeomorphic splines, and dynamical systems. © 2002 Elsevier Science Ltd. All rights reserved

  • 22.
    Ekholm, Tomas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Kovarik, Hynek
    Laptev, Ari
    Hardy inequalities for p-Laplacians with Robin boundary conditions2015In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 128, p. 365-379Article in journal (Refereed)
    Abstract [en]

    In this paper we study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals ((p-1)/p)(p) whenever Dirichlet boundary conditions are imposed on a subset of the boundary of non-zero measure. We also discuss some generalizations to non-convex domains.

  • 23.
    Enstedt, M.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Melgaard, M.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Existence of a solution to Hartree-Fock equations with decreasing magnetic fields2008In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 69, no 7, p. 2125-2141Article in journal (Refereed)
    Abstract [en]

    In the presence of an external magnetic field, we prove existence of a ground state within the Hartree-Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge Z of K nuclei exceeds N - 1, where N is the number of electrons. In the opposite direction, no ground state exists if N > ; 2Z + K.

  • 24.
    Euler, Marianna
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Euler, Norbert
    n-Dimensional real wave equations and the D’Alembert-Hamilton system2001In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 47, no 8, p. 5125-5133Article in journal (Refereed)
    Abstract [en]

    We reduce the nonlinear wave equation □nu = αF[exp(βu)] to ordinary differential equtions and construct exact solutions, by the use of a compatible d'Alembert-Hamilton system. The solutions of these ordinary differential equations, together with the solutions of the corresponding d'Alembert-Hamilton equations, provide a rich class of exact solutions of the multidimensional wave equations. The wave equations are studied in n-dimensional Minkowski space.

  • 25.
    Euler, Norbert
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lindblom, Ove
    Luleå tekniska universitet.
    On discrete velocity Boltzmann equations and the Painlevé analysis2001In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 47, no 2, p. 1407-1412Article in journal (Refereed)
    Abstract [en]

    The multidimensional Bateman equation is investigated to construct explicit solutions of two discrete velocity Boltzmann equations. The Painleve expansion and the general implicit solution are used to construct the solutions in (1 + 1) and (1 + 2) dimensions, respectively. Both these systems of partial differential equations do not pass the Painleve test for integrability.

  • 26.
    Ferm, Lars
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Efficiency in the adaptive solution of inviscid compressible flow problems2001In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 47, p. 3467-3478Article in journal (Refereed)
  • 27.
    Galaktionov, V A
    et al.
    University of Bath, England .
    Maz´ya, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Boundary characteristic point regularity for Navier-Stokes equations: Blow-up scaling and Petrovskii-type criterion (a formal approach)2012In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 75, no 12, p. 4534-4559Article in journal (Refereed)
    Abstract [en]

    The three-dimensional (3D) Navier-Stokes equations less thanbrgreater than less thanbrgreater thanu(t) + (u . del)u = -del p + Delta u, divu = 0 in Q(0), (0.1) less thanbrgreater than less thanbrgreater thanwhere u = [u, v, w](T) is the vector field and p is the pressure, are considered. Here, Q(0) subset of R-3 x [-1, 0) is a smooth domain of a typical backward paraboloid shape, with the vertex (0, 0) being its only characteristic point: the plane {t = 0} is tangent to. partial derivative Q(0) at the origin, and other characteristics for t is an element of [0,-1) intersect. partial derivative Q(0) transversely. Dirichlet boundary conditions on the lateral boundary. partial derivative Q(0) and smooth initial data are prescribed: less thanbrgreater than less thanbrgreater thanu = 0 on. partial derivative Q(0), and u(x, -1) = u(0)(x) in less thanbrgreater than less thanbrgreater thanQ(0) boolean AND {t = -1} (div u(0) = 0). (0.2) less thanbrgreater than less thanbrgreater thanExistence, uniqueness, and regularity studies of (0.1) in non-cylindrical domains were initiated in the 1960s in pioneering works by Lions, Sather, Ladyzhenskaya, and Fujita-Sauer. However, the problem of a characteristic vertex regularity remained open. less thanbrgreater than less thanbrgreater thanIn this paper, the classic problem of regularity (in Wieners sense) of the vertex (0, 0) for (0.1), (0.2) is considered. Petrovskiis famous "2 root log log-criterion of boundary regularity for the heat equation (1934) is shown to apply. Namely, after a blow-up scaling and a special matching with a boundary layer near. partial derivative Q(0), the regularity problem reduces to a 3D perturbed nonlinear dynamical system for the first Fourier-type coefficients of the solutions expanded using solenoidal Hermite polynomials. Finally, this confirms that the nonlinear convection term gets an exponentially decaying factor and is then negligible. Therefore, the regularity of the vertex is entirely dependent on the linear terms and hence remains the same for Stokes and purely parabolic problems. less thanbrgreater than less thanbrgreater thanWell-posed Burnett equations with the minus bi-Laplacian in (0.1) are also discussed.

  • 28.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Megretski, Alexandre
    Analysis and computation of limit cycles for systems with separable nonlinearities2008In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 69, no 12, p. 4674-4693Article in journal (Refereed)
    Abstract [en]

    The variational system obtained by linearizing a dynamical system along a limit cycle is always non-invertible. This follows because the limit cycle is only a unique modulo time translation. It is shown that questions such as uniqueness, robustness, and computation of limit cycles can be addressed using a right inverse of the variational system. Small gain arguments are used in the analysis.

  • 29. Karakhanyan, A. L.
    et al.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Boundary behaviour for a singular perturbation problem2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 138, p. 176-188Article in journal (Refereed)
    Abstract [en]

    In this paper we study the boundary behaviour of the family of solutions (uε) to singular perturbation problem δuε=βε(uε),(divides)uε(divides)≤1 in B1+=(xn>0)∩((divides)x(divides)<1), where a smooth boundary data f is prescribed on the flat portion of ∂B1+. Here βε((dot operator))=1εβ((dot operator)ε),β∈C0∞(0,1),β≥0,∫01β(t)=M>0 is an approximation of identity. If ∇f(z)=0 whenever f(z)=0 then the level sets ∂(uε>0) approach the fixed boundary in tangential fashion with uniform speed. The methods we employ here use delicate analysis of local solutions, along with elaborated version of the so-called monotonicity formulas and classification of global profiles.

  • 30.
    Khrennikov, Andrei
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Mukhamedov, Farrukh
    On uniqueness of Gibbs measurefor p-adic countable state Potts model on the Cayley tree.2009In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 11, p. 5327-5331Article in journal (Refereed)
  • 31. Kim, S.
    et al.
    Lee, K. -A
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    An elliptic free boundary arising from the jump of conductivity2017In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 161, p. 1-29Article in journal (Refereed)
    Abstract [en]

    In this paper we consider a quasilinear elliptic PDE, div(A(x,u)∇u)=0, where the underlying physical problem gives rise to a jump for the conductivity A(x,u), across a level surface for u. Our analysis concerns Lipschitz regularity for the solution u, and the regularity of the level surfaces, where A(x,u) has a jump and the solution u does not degenerate. In proving Lipschitz regularity of solutions, we introduce a new and unexpected type of ACF-monotonicity formula with two different operators, that might be of independent interest, and surely can be applied in other related situations. The proof of the monotonicity formula is done through careful computations, and (as a byproduct) a slight generalization to a specific type of variable matrix-valued conductivity is presented.

  • 32.
    Lenells, Jonatan
    Baylor University, United States .
    The Degasperis-Procesi equation on the half-line2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 76, no 1, p. 122-139Article in journal (Refereed)
    Abstract [en]

    We analyze a class of initial-boundary value problems for the Degasperis-Procesi equation on the half-line. Assuming that the solution u(x,t) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann-Hilbert problem formulated in the plane of the complex spectral parameter k.

  • 33.
    Lindgren, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Privat, Yannick
    A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition2007In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 67, no 8, p. 2497-2505Article in journal (Refereed)
    Abstract [en]

    We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling's technique, by defining two classes of sub- and super-solutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.

  • 34.
    Lundström, Niklas L P
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Estimates for p-harmonic functions vanishing on a flat2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 18, p. 6852-6860Article in journal (Refereed)
    Abstract [en]

    We study p-harmonic functions in a domain ΩCRn near an m-dimensional plane (an m-flat) Λm, where 0≤mn−1. In particular, let u be a positive p-harmonic function, with n<p, vanishing on a portion of Λm, and suppose that β=(pn+m)/(p−1), with β=1 if p=. We prove, using certain barrier functions, that 

     u ≈ d (x.Λm)8   near Λm.

    The lower bound holds also in the range nm<p. Moreover, uC0,β near Λm and β is the optimal Hölder exponent of u.

  • 35. Medeiros, Everaldo
    et al.
    Perera, Kanishka
    Tintarev, Kyril
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Multiplicity results for problems involving the Hardy-Sobolev operator via Morse theory2010In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 72, no 5, p. 2170-2177Article in journal (Refereed)
    Abstract [en]

    We establish some multiplicity results for a class of boundary value problems involving the Hardy-Sobolev operator using Morse theory. (C) 2009 Elsevier Ltd. All rights reserved.

  • 36.
    Melin, Jan
    et al.
    University of Kalmar, School of Pure and Applied Natural Sciences.
    Hultgren, Anders
    University of Kalmar, Department of Technology.
    On conditions for regularity of solutions for a piecewise linear system2006In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 65, no 12, p. 2277-2301Article in journal (Refereed)
  • 37.
    Nyström, Kaj
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Sande, Olow
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Extension properties and boundary estimates for a fractional heat operator2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 140, p. 29-37Article in journal (Refereed)
    Abstract [en]

    The square root of the heat operator $\sqrt{\partial_t-\Delta}$, can be realized as the Dirichlet to Neumann map of the heat extension of data on $\mathbb R^{n+1}$ to $\mathbb R^{n+2}_+$. In this note we obtain similar characterizations for general fractional powers of the heat operator, $(\partial_t-\Delta)^s$, $s\in (0,1)$. Using the characterizations we derive properties and boundary estimates for parabolic integro-differential equations from purely local arguments in the extension problem.

  • 38.
    Ringkvist, Mattias
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Zhou, Yishao
    Stockholm University, Faculty of Science, Department of Mathematics.
    On Dynamical Behaviour of FitzHugh-Nagumo Systems: revisited2009In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 7-8, p. 2667-2687Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to analyse a general form of the FitzHugh–Nagumo model as completely as possible. The main result is that no more than two limit cycles can be bifurcated from the unique fixed point via Hopf bifurcation, and there exist parameters such that this upper bound is attained. For these parameters, the stability of the inner and outer cycle, together with the unique fixed point is also established. The results are approached through Lyapunov coefficients and rely on a theorem by Andronov and Aleksandrovic [A.A. Andronov, A.A. Aleksandrovic, Theory of Bifurcations of Dynamical System on a Plane, Wiley, 1971]. Based on singular perturbation theory a sufficient condition for existence of a unique stable limit cycle is given under certain assumptions.

  • 39.
    Sjödin, Tomas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    A new approach to Sobolev spaces in metric measure spaces2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 142, p. 194-237Article in journal (Refereed)
    Abstract [en]

    Let (X, d(X), mu) be a metric measure space where X is locally compact and separable and mu is a Borel regular measure such that 0 amp;lt; mu(B(x, r)) amp;lt; infinity for every ball B(x, r) with center x is an element of X and radius r amp;gt; 0. We define chi to be the set of all positive, finite non- zero regular Borel measures with compact support in X which are dominated by mu, and M = X boolean OR {0}. By introducing a kind of mass transport metric d(M) on this set we provide a new approach to first order Sobolev spaces on metric measure spaces, first by introducing such for functions F : X -amp;gt; R, and then for functions f : X -amp;gt; [-infinity, infinity] by identifying them with the unique element F-f : X -amp;gt; R defined by the mean- value integral: Ff(eta) - 1/vertical bar vertical bar eta vertical bar vertical bar integral f d eta. In the final section we prove that the approach gives us the classical Sobolev spaces when we are working in open subsets of Euclidean space R-n with Lebesgue measure. (C) 2016 Elsevier Ltd. All rights reserved.

  • 40.
    Sjödin, Tomas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On the structure of partial balayage2007In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 67, no 1, p. 94-102Article in journal (Refereed)
    Abstract [en]

    We define partial balayage, construct it with classical potential-theoretic methods and establish the so called structure formula in full generality. Finally we give a stochastic construction of partial balayage.

  • 41.
    Strömberg, T.
    et al.
    Luleå University of Technology.
    Ahmadzadeh, Farzaneh
    Mälardalen University, School of Innovation, Design and Engineering, Innovation and Product Realisation.
    Excess action and broken characteristics for Hamilton-Jacobi equations2014In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 110, p. 113-129Article in journal (Refereed)
    Abstract [en]

    We study propagation of singularities for Hamilton-Jacobi equations S t+H(t,x,λS)=0,(t,x)∈(0,∞)×ℝn, by means of the excess Lagrangian action and a related class of characteristics. In a sense, the excess action gauges how far a curve X(t) is from being action minimizing for a given viscosity solution S(t,x) of the Hamilton-Jacobi equation. Broken characteristics are defined as curves along which the excess action grows at the slowest pace possible. In particular, we demonstrate that broken characteristics carry the singularities of the viscosity solution.

  • 42.
    Strömberg, Thomas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    A counterexample to uniqueness of generalized characteristics in Hamilton-Jacobi theory2011In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 7, p. 2758-2762Article in journal (Refereed)
    Abstract [en]

    The notion of generalized characteristics plays a pivotal role in the study of propagation of singularities for Hamilton{Jacobi equations. This note gives an example of nonuniqueness of forward generalized characteristics emanating from a given point.

  • 43.
    Strömberg, Thomas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On a viscous Hamilton-Jacobi equation with an unbounded potential term2010In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 73, no 6, p. 1802-1811Article in journal (Refereed)
    Abstract [en]

    We present comparison, uniqueness and existence results for unbounded solutions of a viscous Hamilton-Jacobi or eikonal equation. The equation includes an unbounded potential term V(x) subject to a quadratic upper bound. The results are obtained through a tailor-made change of variables in combination with the Hopf-Cole transformation. An integral representation formula for the solution of the Cauchy problem is derived in the case where V(x)=ω2x2/2

  • 44.
    Strömberg, Thomas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Propagation of singularities along broken characteristics2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 85, p. 93-109Article in journal (Refereed)
    Abstract [en]

    This paper contributes to the analysis of propagation of singularities for semiconcave solutions of Hamilton–Jacobi equations. Under certain conditions, we establish the existence and uniqueness of certain broken characteristics termed strong characteristics. If u is a viscosity solution of a Hamilton–Jacobi equation, then strong characteristics carry the singularities of u.

  • 45.
    Strömberg, Thomas
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Ahmadzadeh, Farzaneh
    School of Innovation, Design and Engineering, Mälardalen University.
    Excess action and broken characteristics for Hamilton-Jacobi equations2014In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 110, p. 113-129Article in journal (Refereed)
    Abstract [en]

    We study propagation of singularities for Hamilton–Jacobi equations View the MathML sourceSt+H(t,x,∇S)=0,(t,x)∈(0,∞)×Rn,Turn MathJax onby means of the excess Lagrangian action and a related class of characteristics. In a sense, the excess action gauges how far a curve View the MathML sourceX(t) is from being action minimizing for a given viscosity solution S(t,x)S(t,x) of the Hamilton–Jacobi equation. Broken characteristics are defined as curves along which the excess action grows at the slowest pace possible. In particular, we demonstrate that broken characteristics carry the singularities of the viscosity solution.

1 - 45 of 45
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