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The Dirichlet problem for non‐divergence parabolic equations with discontinuous in time coefficients
Author(s) -
Kozlov Vladimir,
Nazarov Alexander
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910796
Subject(s) - mathematics , sobolev space , divergence (linguistics) , mathematical analysis , bounded function , parabolic partial differential equation , dirichlet problem , domain (mathematical analysis) , boundary (topology) , dirichlet boundary condition , dirichlet distribution , space (punctuation) , boundary value problem , partial differential equation , philosophy , linguistics
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)