The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values

被引：136
作者：
Harjulehto, Petteri [1 ]
Hasto, Peter
Koskenoja, Mika
Varonen, Susanna
机构：
[1] Univ Helsinki, Dept Math & Stat, POB 68, FIN-00014 Helsinki, Finland
[2] NTNU, Dept Math Sci, N-7491 Trondheim, Norway
来源：
POTENTIAL ANALYSIS | 2006年 / 25卷 / 03期
关键词：
variable exponent Sobolev space; zero boundary values; Sobolev capacity; Poincare inequality; Dirichlet energy integral;
D O I：
10.1007/s11118-006-9023-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We define and study variable exponent Sobolev spaces with zero boundary values. This allows us to prove that the Dirichlet energy integral has a minimizer in the variable exponent case. Our results are based on a Poincare-type inequality, which we prove under a certain local jump condition for the variable exponent.
引用
收藏
页码：205 / 222
页数：18
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