Overview of differential equations with non-standard growth

被引：339
作者：
Harjulehto, Petteri [2 ]
Hasto, Peter [1 ]
Le, Ut V. [1 ]
Nuortio, Matti [1 ]
机构：
[1] Univ Oulu, Dept Math Sci, POB 3000, FI-90014 Oulu, Finland
[2] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 12期
基金：
芬兰科学院;
关键词：
Variable exponent; Non-standard growth; Eigenvalue problem; Existence; Uniqueness; Regularity; Harmonic functions; Elliptic equations; Parabolic equations; NONLINEAR ELLIPTIC-EQUATIONS; EXPONENT SOBOLEV SPACES; BOUNDARY-VALUE-PROBLEMS; BLOW-UP SOLUTIONS; VARIABLE EXPONENT; P(X)-LAPLACIAN EQUATIONS; POSITIVE SOLUTIONS; DIRICHLET PROBLEM; WEAK SOLUTIONS; EIGENVALUE PROBLEM;
D O I：
10.1016/j.na.2010.02.033
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Differential equations with non-standard growth have been a very active field of investigation in recent years. In this survey we present an overview of the field, as well as several of the most important results. We consider both existence and regularity questions. Finally, we provide a comprehensive list of papers published to date. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：4551 / 4574
页数：24
相关论文
共 185 条
[1]   New diffusion models in image processing [J].
Aboulaich, R. ;
Meskine, D. ;
Souissi, A. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (04) :874-882
[2]  
Acerbi E, 2005, J REINE ANGEW MATH, V584, P117
[3]   Regularity results for parabolic systems related to a class of non-Newtonian fluids [J].
Acerbi, E ;
Mingione, G ;
Seregin, GA .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2004, 21 (01) :25-60
[4]   Regularity results for stationary electro-rheological fluids [J].
Acerbi, E ;
Mingione, G .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (03) :213-259
[5]   Regularity results for a class of functionals with non-standard growth [J].
Acerbi, E ;
Mingione, G .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) :121-140
[6]   Mappings of Finite Distortion and PDE with Nonstandard Growth [J].
Adamowicz, Tomasz ;
Hasto, Peter .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (10) :1940-1965
[7]  
AFROUZI GA, 2007, ELECT J DIFFERENTIAL, V177, P1
[8]   Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition [J].
Alkhutov, YA ;
Krasheninnikova, OV .
IZVESTIYA MATHEMATICS, 2004, 68 (06) :1063-1117
[9]  
Alkhutov YA, 1997, DIFF EQUAT+, V33, P1653
[10]  
Alkhutov YA., 2005, Mat. Sb, V196, P3, DOI [10.1070/SM2005v196n02ABEH000875, DOI 10.1070/SM2005V196N02ABEH000875]
12345678910