Global gradient estimates for the p(•)-Laplacian

被引：45

作者：

Diening, L.

Schwarzacher, S.

机构：

[1] Theresienstr. 39

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 106卷

关键词：

Nonlinear Calderon-Zygmund theory; Variable exponents; Generalized Lebesgue and Sobolev spaces; Electrorheological fluids; MAXIMAL-FUNCTION; SPACES; INTEGRABILITY; FUNCTIONALS; REGULARITY; OPERATORS;

D O I：

10.1016/j.na.2014.04.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Calderon-Zygmund type estimates for the non-homogeneous p(center dot)-Laplacian system -div(| Du|(p(center dot)-2Du)) = -div(| G|(p(center dot)-2)G), where p is a variable exponent. We show that |G| p(center dot)epsilon L-q(R-n) boolean AND L-1(R-n) implies |Du|(p(center dot)) epsilon L-q(R-n) boolean AND L-1(R-n) for any q >= 1. We also prove local estimates independent of the size of the domain and introduce new techniques to variable analysis. The paper is an extension of the local estimates of Acerbi-Mingione (2005). (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：70 / 85

页数：16

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