Boundary Regularity under Generalized Growth Conditions

被引：35

作者：

Harjulehto, Petteri ^{[1
]}

Hasto, Peter ^{[1
,2
]}

机构：

[1] Univ Turku, Dept Math & Stat, FI-20014 Turku, Finland

[2] Univ Oulu, Dept Math, FI-90014 Oulu, Finland

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2019年 / 38卷 / 01期

关键词：

Dirichlet energy integral; regular boundary point; minimizer; superminimizer; generalized Orlicz space; Musielak-Orlicz spaces; the weak Harnack inequality; nonstandard growth; variable exponent; double phase; NONSTANDARD GROWTH; SOBOLEV SPACES; ORLICZ SPACES; QUASIMINIMIZERS; FUNCTIONALS; INEQUALITY;

D O I：

10.4171/ZAA/1628

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Dirichlet phi-energy integral with Sobolev boundary values. The function phi has generalized Orlicz growth. Special cases include variable exponent and double phase growths. We show that minimizers are regular at the boundary provided a weak capacity fatness condition is satisfied. This condition is satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.

引用

页码：73 / 96

页数：24

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