Recent developments in problems with nonstandard growth and nonuniform ellipticity

被引：224
作者：
Mingione, Giuseppe [1 ]
Radulescu, Vicentiu [2 ]
机构：
[1] Univ Parma, Dipartimento SMFI, Viale Sci 53-A, I-43124 Parma, Italy
[2] Univ Craiova, Dept Math, Craiova 200585, Romania
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 501卷 / 01期
关键词：
Regularity; Nonstandard growth conditions; Nonuniform ellipticity; INTERIOR GRADIENT BOUNDS; MUSIELAK-ORLICZ SPACES; PARABOLIC EQUATIONS; LAVRENTIEV PHENOMENON; WEAK SOLUTIONS; DIFFERENTIAL-EQUATIONS; RENORMALIZED SOLUTIONS; VARIATIONAL INTEGRALS; LIPSCHITZ REGULARITY; HIGHER INTEGRABILITY;
D O I：
10.1016/j.jmaa.2021.125197
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide an overview of recent results concerning elliptic variational problems with nonstandard growth conditions and related to different kinds of nonuniformly elliptic operators. Regularity theory is at the center of this paper. (c) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页数：41
相关论文
共 219 条
[1]   Relaxation of convex functional:: The gap problem [J].
Acerbi, E ;
Bouchitté, G ;
Fonseca, I .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2003, 20 (03) :359-390
[2]   Regularity results for stationary electro-rheological fluids [J].
Acerbi, E ;
Mingione, G .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (03) :213-259
[3]   Gossez's approximation theorems in Musielak-Orlicz-Sobolev spaces [J].
Ahmida, Youssef ;
Chlebicka, Iwona ;
Gwiazda, Piotr ;
Youssfi, Ahmed .
JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 275 (09) :2538-2571
[4]   Fully anisotropic elliptic problems with minimally integrable data [J].
Alberico, Angela ;
Chlebicka, Iwona ;
Cianchi, Andrea ;
Zatorska-Goldstein, Anna .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (06)
[5]   BEHAVIOR OF SOLUTIONS OF THE DIRICHLET PROBLEM FOR THE p(x)-LAPLACIAN AT A BOUNDARY POINT [J].
Alkhutov, Yu A. ;
Surnachev, M. D. .
ST PETERSBURG MATHEMATICAL JOURNAL, 2020, 31 (02) :251-271
[6]   A compact embedding result for anisotropic Sobolev spaces associated to a strip-like domain and some applications [J].
Alves, Claudianor ;
Bisci, Giovanni Molica .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 501 (01)
[7]   Multiplicity of positive solutions for afractional p&q-Laplacian problem in RN [J].
Ambrosio, Vincenzo ;
Isernia, Teresa .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 501 (01)
[8]   Fractional double-phase patterns: concentration and multiplicity of solutions [J].
Ambrosio, Vincenzo ;
Radulescu, Vicentiu D. .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2020, 142 :101-145
[9]  
[Anonymous], JAHRESBER DTSCH MATH
[10]   Gradient estimates for multi-phase problems [J].
Baasandorj, Sumiya ;
Byun, Sun-Sig ;
Oh, Jehan .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (03)
12345678910