Boundedness of solutions of the non-uniformly convex, non-standard growth Laplacian

被引：1

作者：

Harjulehto, P. ^{[2
]}

Hasto, P. ^{[1
]}

Latvala, V. ^{[3
]}

机构：

[1] Univ Oulu, Dept Math Sci, FI-90014 Oulu, Finland

[2] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland

[3] Univ Eastern Finland, Dept Math & Phys, FI-80101 Joensuu, Finland

来源：

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

基金：

芬兰科学院;

关键词：

non-standard growth; variable exponent; Laplace equation; Dirichlet energy; local boundedness; solution; Hausdorff measure; capacity; VARIABLE EXPONENT; ELLIPTIC-EQUATIONS; LEBESGUE SPACES; SOBOLEV SPACES; REGULARITY; FUNCTIONALS; MINIMIZERS; INEQUALITY; OPERATORS;

D O I：

10.1080/17476931003728446

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the variable exponent p(.)-Laplace equation -Delta(p(.))u = 0 when p attains the value 1. We prove a removability result and local boundedness for its solutions and obtain a weak continuity result. Our results also apply to (A, B)-solutions of p(.)-growth.

引用

页码：643 / 657

页数：15

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