Global regularity and stability of solutions to elliptic equations with nonstandard growth

被引：10

作者：

Eleuteri, Michela ^{[2
]}

Harjulehto, Petteri ^{[1
]}

Lukkari, Teemu ^{[3
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, POB 68, FI-00014 Helsinki, Finland

[2] Dipartimento Matemat Trento, I-38123 Povo, Trento, Italy

[3] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2011年 / 56卷 / 7-9期

基金：

芬兰科学院;

关键词：

global higher integrability; boundary regularity; stability of solutions; Sobolev-Poincare inequality; Hardy inequality; EXPONENT SOBOLEV SPACES; GENERALIZED LEBESGUE; INTEGRABILITY; INEQUALITIES; FUNCTIONALS;

D O I：

10.1080/17476930903568399

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the regularity properties of solutions to elliptic equations similar to the p(.)-Laplacian. Our main results are a global reverse Holder inequality, Holder continuity up to the boundary and stability of solutions with respect to continuous perturbations in the variable growth exponent. We assume that the complement of the domain is uniformly fat in a capacitary sense. As technical tools, we derive a capacitary Sobolev-Poincare inequality, and a version of Hardy's inequality.

引用

页码：599 / 622

页数：24

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