Annali di Matematica Pura ed Applicata

, Volume 188, Issue 2, pp 333–358

Global gradient estimates for degenerate parabolic equations in nonsmooth domains

Article

Abstract

This paper studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates for the gradient. The results extend to the parabolic systems as well. The higher integrability estimates provide a useful tool in several applications.

Keywords

Boundary value problem Gehring lemma Global higher integrability Initial value problem Reverse Hölder inequality 

Mathematics Subject Classification (2000)

35K60 35K55 35K15 49N60 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institute of MathematicsHelsinki University of TechnologyTKKFinland

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