Global higher integrability for parabolic quasiminimizers in nonsmooth domains

Original Article

Abstract

We study the global higher integrability of the gradient of a parabolic quasiminimizer with quadratic growth conditions. We show that if the lateral boundary satisfies a capacity density condition and if boundary and initial values are smooth enough, then quasiminimizers globally belong to a higher Sobolev space than assumed a priori. We derive estimates near the lateral and the initial boundaries.

Mathematics Subject Classification (2000)

Primary: 35K60 Secondary: 35K15 35K55 49N60 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institute of MathematicsHelsinki University of TechnologyHelsinkiFinland

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