Higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Erhardt, Andre H.¹ 

[1] Univ Hohenheim, Inst Appl Math & Stat, D-70599 Stuttgart, Germany

关键词: Higher integrability;    Nonlinear parabolic problems;    Irregular obstacle;    Localizable solution;    Nonstandard growth;   

DOI  :  10.1016/j.jmaa.2015.11.028

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free