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.
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页码：345 / 359
页数：15
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