Generalized Orlicz spaces and related PDE

被引：83

作者：

Harjulehto, Petteri ^{[1
]}

Hasto, Peter ^{[1
]}

Klen, Riku ^{[1
]}

机构：

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 143卷

关键词：

Musielak-Orlicz spaces; Orlicz space; Sobolev space; Variable exponent; Poincare inequality; Dirichlet energy integral; Existence of solution; Nonstandard growth; VARIABLE EXPONENT; RIESZ-POTENTIALS; FUNCTIONALS; INEQUALITIES; REGULARITY;

D O I：

10.1016/j.na.2016.05.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the boundedness of the maximal operator in generalized Orlicz spaces defined on subsets of R-n. The proof is based on an extension result for Phi-functions. We study generalized Sobolev-Orlicz spaces and establish density of smooth functions and the Poincare inequality. As applications we establish the existence of solutions of the phi-Laplace equation with zero and non-zero right-hand side. Further, we systematize assumptions for Phi-functions and prove several basic tools needed for the study of differential equations of generalized Orlicz growth. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：155 / 173

页数：19