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  • 1.
    Adamowicz, Tomasz
    et al.
    Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures2016In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, no 2, p. 623-658Article in journal (Refereed)
    Abstract [en]

    We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-domains), we show the boundary Harnack inequality for p(⋅)-harmonic functions under the assumption that the variable exponent p is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson-type estimate for p(⋅)-harmonic functions in NTA domains in Rn and provide lower and upper growth estimates and a doubling property for a p(⋅)-harmonic measure.

  • 2. Adimurthi,
    et al.
    Tintarev, Kyril
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Hardy inequalities for weighted Dirac operator2010In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 189, no 2, p. 241-251Article in journal (Refereed)
    Abstract [en]

    An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight r(-b) for functions in R-n. The exact Hardy constant c(b) = c(b) (n) is found and generalized minimizers are given. The constant cb vanishes on a countable set of b, which extends the known case n = 2, b = 0 which corresponds to the trivial Hardy inequality in R-2. Analogous inequalities are proved in the case c(b) = 0 under constraints and, with error terms, for a bounded domain.

  • 3. Bjerklöv, Kristian
    et al.
    Damanik, David
    Johnson, Russell
    Lyapunov exponents of continuous Schrodinger cocycles over irrational rotations2008In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 187, no 1, p. 1-6Article in journal (Refereed)
    Abstract [en]

    We consider the Lyapunov exponent of those continuous SL( 2, R)-valued cocycles over irrational rotations that appear in the study of Schrodinger operators and prove generic results related to large coupling asymptotics and uniform convergence.

  • 4. Cinti, Chiara
    et al.
    Nyström, Kaj
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Polidoro, Sergio
    A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form2012In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 191, no 1, p. 1-23Article in journal (Refereed)
    Abstract [en]

    We consider non-negative solutions to a class of second-order degenerate Kolmogorov operators of the form \fancyscriptL=∑i,j=1mai,j(z)∂xixj+∑i=1mai(z)∂xi+∑i,j=1Nbi,jxi∂xj−∂t, where z = (x, t) belongs to an open set Ω⊂RN×R , and 1 ≤ m ≤ N. Let z˜∈Ω , let K be a compact subset of Ω−− , and let Σ⊂∂Ω be such that K∩∂Ω⊂Σ . We give sufficient geometric conditions for the validity of the following Carleson type estimate. There exists a positive constant C K , depending only on Ω,Σ,K,z˜ and on \fancyscriptL , such that supKu≤CKu(z˜), for every non-negative solution u of \fancyscriptLu=0 in Ω such that u∣Σ=0 .

  • 5. Cinti, Chiara
    et al.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Polidoro, Sergio
    A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form2012In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 191, no 1, p. 1-23Article in journal (Refereed)
    Abstract [en]

    We consider non-negative solutions to a class of second-order degenerate Kolmogorov operators of the form L=Sigma(m)(i,j=1)a(i,j)(z)partial derivative(xixj)+Sigma(m)(i=1)a(i)(z)partial derivative(xi)+Sigma(N)(i,j=1)b(i,j)x(i)partial derivative(xj)-partial derivative(t), where z = (x, t) belongs to an open set Omega subset of R-N x R, and 1 <= m <= N. Let (z) over bar is an element of Omega, let K be a compact subset of (Omega) over bar, and let Sigma subset of partial derivative Omega be such that K boolean AND partial derivative Omega subset of Sigma. give sufficient geometric conditions for the validity of the following Carleson type estimate. There exists a positive constant C-K, depending only on Omega, Sigma, K, (z) over tilde and on L, such that sup(K) u <= C(K)u((z) over tilde), for every non-negative solution u of Lu = 0 in Omega such that u|(Sigma) = 0.

  • 6. Clapp, Mónica
    et al.
    Pistoia, Angela
    Szulkin, Andrzej
    Stockholm University, Faculty of Science, Department of Mathematics.
    Ground states of critical and supercritical problems of Brezis-Nirenberg type2016In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, no 5, p. 1787-1802Article in journal (Refereed)
    Abstract [en]

    We study the existence of symmetric ground states to the supercritical problem -Delta v = lambda v + vertical bar v vertical bar(p-2) v in Omega, v = 0 on partial derivative Omega in a domain of the form Omega = {( y, z) is an element of Rk+ 1 x RN- k-1 : (vertical bar y vertical bar, z) is an element of Theta}, where Theta is a bounded smooth domain such that (Theta) over bar subset of (0,infinity) x RN-k-1, 1 <= k <= N - 3, lambda is an element of R, and p = 2(N-k)/N-k-2 is the (k + 1)-st critical exponent. We show that symmetric ground states exist for. in some interval to the left of each symmetric eigenvalue and that no symmetric ground states exist in some interval (-infinity, lambda(*)) with lambda(*) > 0 if k >= 2. Related to this question is the existence of ground states to the anisotropic critical problem -div(a(x)del u) = lambda b(x) u + c(x) vertical bar u vertical bar(2*-2) u in Theta, u = 0 on partial derivative Theta, where a, b, c are positive continuous functions on (Theta) over bar. We give a minimax characterization for the ground states of this problem, study the ground state energy level as a function of., and obtain a bifurcation result for ground states.

  • 7. Figalli, Alessio
    et al.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A general class of free boundary problems for fully nonlinear parabolic equations2015In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 194, no 4, p. 1123-1134Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the fully nonlinear parabolic free boundary problem { F(D(2)u) - partial derivative(t)u = 1 a.e. in Q(1) boolean AND Omega vertical bar D(2)u vertical bar + vertical bar partial derivative(t)u vertical bar <= K a.e. in Q(1)\Omega, where K > 0 is a positive constant, and Omega is an (unknown) open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W-x(2,) (n) boolean AND W-t(1,) (n) solutions are locally C-x(1,) (1) boolean AND C-t(0,) (1) inside Q(1). A key starting point for this result is a new BMO-type estimate, which extends to the parabolic setting the main result in Caffarelli and Huang (Duke Math J 118(1): 1-17, 2003). Once optimal regularity for u is obtained, we also show regularity for the free boundary partial derivative Omega boolean AND Q(1) under the extra condition that Omega superset of{u not equal 0}, and a uniform thickness assumption on the coincidence set {u = 0}.

  • 8.
    Karakhanyan, Aram L.
    et al.
    Univ Edinburgh, Sch Math, Mayfield Rd,Kings Bldg, Edinburgh EH9 3JZ, Midlothian, Scotland..
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On a conjecture of De Giorgi related to homogenization2017In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 196, no 6, p. 2167-2183Article in journal (Refereed)
    Abstract [en]

    For a periodic vector field F, let solve the dynamical system dX(epsilon)/dt = F (X-epsilon/epsilon). In (Set Valued Anal 2(1-2):175-182, 1994) Ennio De Giorgi enquiers whether from the existence of the limit one can conclude that . Our main result settles this conjecture under fairly general assumptions on F, which in some cases may also depend on t-variable. Once the above problem is solved, one can apply the result to the corresponding transport equation, in a standard way. This is also touched upon in the text to follow.

  • 9.
    Kolyada, Viktor
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms2019In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 198, no 2, p. 615-637Article in journal (Refereed)
    Abstract [en]

    We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvement of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin-type estimates of Fourier transforms for functions in Sobolev spaces W11(Rn).

  • 10.
    Kolyada, Viktor
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Optimal relationships between L-p-norms for the Hardy operator and its dual2014In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 2, p. 423-430Article in journal (Refereed)
    Abstract [en]

    We obtain sharp two-sided inequalities between -norms of functions and , where is the Hardy operator, is its dual, and is a nonnegative measurable function on In an equivalent form, it gives sharp constants in the two-sided relationships between -norms of functions and , where is a nonnegative nonincreasing function on with In particular, it provides an alternative proof of a result obtained by Kruglyak and Setterqvist (Proc Am Math Soc 136:2005-2013, 2008) for and by Boza and Soria (J Funct Anal 260:1020-1028, 2011) for all , and gives a sharp version of this result for 1 < p < 2.

  • 11.
    Kolyada, Viktor
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Soria, Javier
    Hölder type inequalities in Lorentz spaces2010In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 189, no 3, p. 523-538Article in journal (Refereed)
  • 12.
    Kozlov, Vladimir
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Maz´ya, Vladimir G.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Asymptotic formula for solutions to elliptic equations near the Lipschitz boundary2005In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 184, no 2, p. 185-213Article in journal (Refereed)
    Abstract [en]

    [No abstract available]

  • 13.
    Kozlov, Vladimir
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Tkachev, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Vakulenko, Sergey
    St. Petersburg National Research University of Information Technologies, Saint Petersburg, Russia.
    Wennergren, Uno
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Biology. Linköping University, Faculty of Science & Engineering.
    Global stability and persistence of complex foodwebs2019In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 198, no 3Article in journal (Refereed)
    Abstract [en]

    We develop a novel approach to study the global behaviour of large foodwebs for ecosystems where several species share multiple resources. The model extends and generalizes some previous works and takes into account self-limitation. Under certain explicit conditions, we establish the global convergence and persistence of solutions.

  • 14.
    Lundström, Niklas L P
    et al.
    Department of Mathematics, Uppsala University, Sweden.
    Nyström, Kaj
    Department of Mathematics, Uppsala University, Sweden.
    Olofsson, Marcus
    Department of Mathematics, Uppsala University, Sweden.
    Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type2014In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 4, p. 1213-1247Article in journal (Refereed)
    Abstract [en]

    In this paper we study the system where . A special case of this type of system of variational inequalities with terminal data occurs in the context of optimal switching problems. We establish a general comparison principle for viscosity sub- and supersolutions to the system under mild regularity, growth, and structural assumptions on the data, i.e., on the operator and on continuous functions , , and . A key aspect is that we make no sign assumption on the switching costs and that is allowed to depend on as well as . Using the comparison principle, the existence of a unique viscosity solution to the system is constructed as the limit of an increasing sequence of solutions to associated obstacle problems. Having settled the existence and uniqueness, we subsequently focus on regularity of beyond continuity. In this context, in particular, we assume that belongs to a class of second-order differential operators of Kolmogorov type of the form: where . The matrix is assumed to be symmetric and uniformly positive definite in . In particular, uniform ellipticity is only assumed in the first coordinate directions, and hence, may be degenerate.

  • 15.
    Lundström, Niklas
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Nyström, Kaj
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Olofsson, Marcus
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type2014In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 4, p. 1213-1247Article in journal (Refereed)
  • 16.
    Nacinovich, Mauro
    et al.
    Dipartimento di Matematica, II Universita` di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma (Italy).
    Porten, Egmont
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics. Instytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach, Kielce, Poland.
    Weak q-concavity conditions for CR-manifolds2017In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 196, no 5, p. 1779-1817Article in journal (Refereed)
    Abstract [en]

    We introduce various notions of q-pseudo-concavity for abstract CR manifolds, and we apply these notions to the study of hypoellipticity, maximum modulus principle and Cauchy problems for CR functions.

  • 17.
    Oliaro, Alessandro
    et al.
    Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino (TO), Italy.
    Rodino, Luigi
    Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino (TO), Italy.
    Wahlberg, Patrik
    Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino (TO), Italy.
    Almost periodic pseudodifferential operators and Gevrey classes2012In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 191, no 4, p. 725-760Article in journal (Refereed)
    Abstract [en]

    We study almost periodic pseudodifferential operators acting on almost periodic functions G s ap (R d )  of Gevrey regularity index s ≥ 1. We prove that almost periodic operators with symbols of Hörmander type S m ρ,δ   satisfying an s-Gevrey condition are continuous on G s ap (R d )  provided 0 < ρ ≤ 1, δ = 0 and s ρ ≥ 1. A calculus is developed for symbols and operators using a notion of regularizing operator adapted to almost periodic Gevrey functions and its duality. We apply the results to show a regularity result in this context for a class of hypoelliptic operators.

  • 18. Perera, Kanishka
    et al.
    Tintarev, Kyril
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    On the second minimax level of the scalar field equation and symmetry breaking2015In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 194, no 1, p. 131-144Article in journal (Refereed)
    Abstract [en]

    We study the second minimax level lambda(2) of the eigenvalue problem for the scalar field equation in R-N. We prove the existence of an eigenfunction at the level lambda(2) when the potential near infinity approaches the constant level from below no faster than e(-epsilon vertical bar x vertical bar). We also consider questions about the nodality of eigenfunctions at this level and establish symmetry breaking at the levels 2, ..., N.

  • 19. Tertikas, A.
    et al.
    Tintarev, Kyril
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    On existence of minimizers for the Hardy-Sobolev-Maz'ya inequality2007In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 186, no 4, p. 645-662Article in journal (Refereed)
    Abstract [en]

    We show existence of minimizers for the Hardy-Sobolev-Maz'ya inequality in Rm+n\R-n when either m > 2, n >= 1 or m=1, n >= 3.

  • 20.
    Thim, Johan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Asymptotics and inversion of Riesz potentials through decomposition in radial and spherical parts2016In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, no 2, p. 323-341Article in journal (Refereed)
    Abstract [en]

    It is known that radial symmetry is preserved by the Riesz potential operators and also by the hypersingular Riesz fractional derivatives typically used for inversion. In this paper, we collect properties, asymptotics, and estimates for the radial and spherical parts of Riesz potentials and for solutions to the Riesz potential equation of order one. Sharp estimates for spherical functions are provided in terms of seminorms, and a careful analysis of the radial part of a Riesz potential is carried out in elementary terms. As an application, we provide a two weight estimate for the inverse of the Riesz potential operator of order one acting on spherical functions.

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