Calculus of Variations and Partial Differential Equations

, Volume 31, Issue 1, pp 75–98

Global higher integrability for parabolic quasiminimizers in nonsmooth domains

Original Article

DOI: 10.1007/s00526-007-0106-9

Cite this article as:
Parviainen, M. Calc. Var. (2008) 31: 75. doi:10.1007/s00526-007-0106-9

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: 35K60Secondary: 35K1535K5549N60

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institute of MathematicsHelsinki University of TechnologyHelsinkiFinland