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Anisotropic parabolic equations with variable nonlinearity

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jul 2009 English Publisher:Universitat Autonoma de BarcelonaJournal:Publicacions Matemàtiques, volume 53, pages 355-399 (issn: 0214-1493, Copyright policy )
Authors: Antontsev, S.; Shmarev, S.;

doi: 10.5565/publmat_53209_04

Anisotropic parabolic equations with variable nonlinearity

Abstract

We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions. Equations of this class generalize the evolutional p(x, t)-Laplacian. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time L∞ bounds for the weak solutions.

Related Organizations
Keywords

Anisotropic nonlinearity, 35K55, nonstandard growth conditions, Nonlinear parabolic equation, 35K65, Nonstandard growth conditions, anisotropic nonlinearity

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
164
Top 1%
Top 1%
Top 10%
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