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Oblique derivative problem for non-divergence parabolic equations with discontinuous in time coefficients
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
St.-Petersburg Department of Steklov Institute, St.-Petersburg, Russia; St Petersburg State University, Russia.
2014 (English)In: Proceedings of the St. Petersburg Mathematical Society Volume XV: Advances in Mathematical Analysis of Partial Differential Equations / [ed] Darya Apushkinskaya; Alexander I. Nazarov, American Mathematical Society (AMS), 2014, , 21 p.177-191 p.Chapter in book (Other academic)
Abstract [en]

We consider an oblique derivative problem for non-divergence parabolic equations with discontinuous in t coefficients in a half-space. We obtain weighted coercive estimates of solutions in anisotropic Sobolev spaces. We also give an application of this result to linear parabolic equations in a bounded domain. In particular, if the boundary is of class C1,δ , δ∈(0,1] , then we present a coercive estimate of solutions in weighted anisotropic Sobolev spaces, where the weight is a power of the distance to the boundary.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2014. , 21 p.177-191 p.
, American Mathematical Society. Translations, ISSN 0065-9290 ; 2 Vol. 232
National Category
Mathematical Analysis
URN: urn:nbn:se:liu:diva-121596ISBN: 9781470415518ISBN: 1470415518OAI: diva2:857117
Available from: 2015-09-28 Created: 2015-09-28 Last updated: 2015-10-05Bibliographically approved

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