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.
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页码：70 / 85
页数：16
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