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

共 31 条

[1] On some new non-linear diffusion models for the image filtering [J].

Alaoui, Mohammed Kbiri ;

Nabil, Tamer ;

Altanji, Mohamed .

APPLICABLE ANALYSIS, 2014, 93 (02) :269-280

[2]

[Anonymous], 2013, INT SERIES NUMERICAL

[3]

[Anonymous], TOHOKU MATH IN PRESS

[4] NON-AUTONOMOUS FUNCTIONALS, BORDERLINE CASES AND RELATED FUNCTION CLASSES [J].

Baroni, P. ;

Colombo, M. ;

Mingione, G. .

ST PETERSBURG MATHEMATICAL JOURNAL, 2016, 27 (03) :347-379

[5] Harnack inequalities for double phase functionals [J].

Baroni, Paolo ;

Colombo, Maria ;

Mingione, Giuseppe .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 :206-222

[6]

BOJARSKI B, 1988, LECT NOTES MATH, V1351, P52

[7] Variable exponent, linear growth functionals in image restoration [J].

Chen, Yunmei ;

Levine, Stacey ;

Rao, Murali .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 66 (04) :1383-1406

[8] Calderon-Zygmund estimates and non-uniformly elliptic operators [J].

Colombo, Maria ;

Mingione, Giuseppe .

JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 270 (04) :1416-1478

[9] Bounded Minimisers of Double Phase Variational Integrals [J].

Colombo, Maria ;

Mingione, Giuseppe .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2015, 218 (01) :219-273

[10] Regularity for Double Phase Variational Problems [J].

Colombo, Maria ;

Mingione, Giuseppe .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2015, 215 (02) :443-496

← 1 2 3 4 →