Published Paper

Inserted: 27 jan 2014
Last Updated: 19 apr 2016

Journal: J. Math. Anal. Appl.
Volume: 435
Number: 2
Pages: 1772–1803
Year: 2016
Doi: 10.1016/j.jmaa.2015.11.028

Abstract:

The aim of this paper is to derive the self-improving property of integrability for the spatial gradient of solutions to degenerate parabolic obstacle problem with irregular obstacles and $p(x,t)$-nonstandard growth. More precisely, we prove that the spatial gradient of the solution is integrable to a larger power than the natural one determined by the structural assumptions on the involved differential operator.

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• Erhardt-Higher-integarbility-obstacle-p@z@-preprint.pdf