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.
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Parviainen, M. Global higher integrability for parabolic quasiminimizers in nonsmooth domains. Calc. Var. 31, 75–98 (2008). https://doi.org/10.1007/s00526-007-0106-9
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DOI: https://doi.org/10.1007/s00526-007-0106-9