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The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
St Petersburg State University.
2009 (English)In: MATHEMATISCHE NACHRICHTEN, ISSN 0025-584X, Vol. 282, no 9, 1220-1241 p.Article in journal (Refereed) Published
Abstract [en]

We consider the Dirichlet problem for non-divergence parabolic equation with discontinuous in t coefficients in a half space. The main result is weighted coercive estimates of solutions in anisotropic Sobolev spaces. We give an application of this result to linear and quasi-linear parabolic equations in a bounded domain. In particular, if the boundary is of class C-1,C-delta, delta is an element of [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
2009. Vol. 282, no 9, 1220-1241 p.
Keyword [en]
Non-divergence parabolic equations, discontinuous in time coefficients, Dirichlet problem, coercive estimates, anisotropic Sobolev spaces
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-51278DOI: 10.1002/mana.200910796OAI: oai:DiVA.org:liu-51278DiVA: diva2:273925
Available from: 2009-10-26 Created: 2009-10-26 Last updated: 2009-10-26

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Kozlov, Vladimir

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