Global gradient estimates for $p(x)$-Laplace equation in non-smooth domains

Chao Zhang; Lihe Wang; Shulin Zhou; Yun-Ho Kim

doi:10.3934/cpaa.2014.13.2559

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Global gradient estimates for $p(x)$-Laplace equation in non-smooth domains

Journal article

Open access

Peer reviewed

Global gradient estimates for $p(x)$-Laplace equation in non-smooth domains

Chao Zhang, Lihe Wang, Shulin Zhou and Yun-Ho Kim

Communications on pure and applied analysis, Vol.13(6), pp.2559-2587

07/2014

DOI: 10.3934/cpaa.2014.13.2559

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Abstract

In this paper we consider the global gradient estimates for weak solutions of $p(x)$-Laplacian type equation with small BMO coefficients in a $\delta$-Reifenberg flat domain. The modified Vitali covering lemma, good $\lambda$-inequalities, the maximal function technique and the appropriate localization method are the main analytical tools. The global Caldéron--Zygmund theory for such equations is obtained. Moreover, we generalize the regularity estimates in the Lebesgue spaces to the Orlicz spaces.

Details

Title: Subtitle: Global gradient estimates for $p(x)$-Laplace equation in non-smooth domains
Creators: Chao Zhang
Lihe Wang
Shulin Zhou
Yun-Ho Kim
Resource Type: Journal article
Publication Details: Communications on pure and applied analysis, Vol.13(6), pp.2559-2587
DOI: 10.3934/cpaa.2014.13.2559
ISSN: 1534-0392
eISSN: 1553-5258
Language: English
Date published: 07/2014
Academic Unit: Mathematics
Record Identifier: 9984083294202771

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