The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients
2009 (English)In: MATHEMATISCHE NACHRICHTEN, ISSN 0025-584X, Vol. 282, no 9, 1220-1241 p.Article in journal (Refereed) Published
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.
Non-divergence parabolic equations, discontinuous in time coefficients, Dirichlet problem, coercive estimates, anisotropic Sobolev spaces
IdentifiersURN: urn:nbn:se:liu:diva-51278DOI: 10.1002/mana.200910796OAI: oai:DiVA.org:liu-51278DiVA: diva2:273925