Harnack's inequality for p(.)-harmonic functions with unbounded exponent p

被引：30

作者：

Harjulehto, Petteri ^{[2
]}

Hasto, Peter ^{[1
]}

Latvala, Visa ^{[3
]}

机构：

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

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

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 352卷 / 01期

关键词：

Non-standard growth; Variable exponent; Laplace equation; Dirichlet energy; Solution; Caccioppoli estimate; VARIABLE EXPONENT; ELLIPTIC-EQUATIONS; LEBESGUE SPACES; SOBOLEV SPACES; REGULARITY; CONTINUITY; MINIMIZERS;

D O I：

10.1016/j.jmaa.2008.05.090

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study properties of the function u = lim(lambda ->infinity)u(lambda), where u(lambda) is the solution of the min{p(.), lambda}-Laplacian Dirichlet problem with bounded Sobolev boundary function. Here p:Omega -> (n, infinity] is a variable exponent such that 1/p is Lipschitz continuous. We derive Bloch-type estimates and using them we prove Harnack's inequality in cases of unbounded but finite exponent. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：345 / 359

页数：15

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