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The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients

✍ Scribed by Vladimir Kozlov; Alexander Nazarov

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 262 KB
Volume: 282
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200910796

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✦ Synopsis

Abstract

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,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 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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