Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems

被引：8
作者：
Beck, Lisa [1 ]
Mingione, Giuseppe [2 ]
机构：
[1] Univ Augsburg, Inst Math, Univ Str 14, D-86159 Augsburg, Germany
[2] Univ Parma, Dipartimento SMFI, Viale Sci 53-A Campus, I-43124 Parma, Italy
来源：
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2019年 / 30卷 / 02期
关键词：
Regularity; non-uniform ellipticity; Lorentz spaces; REGULARITY; GRADIENT; MINIMIZERS; FUNCTIONALS;
D O I：
10.4171/RLM/844
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal criteria for Lipschitz continuity known in the uniformly elliptic one and provide a unified approach between non-uniformly and uniformly elliptic problems.
引用
收藏
页码：223 / 236
页数：14
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[11]   Riesz potential estimates for a general class of quasilinear equations [J].
Baroni, Paolo .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 53 (3-4) :803-846
[12]  
Bildhauer M, 2001, CALC VAR PARTIAL DIF, V13, P537, DOI 10.1007/s005260100090
[13]  
Carozza M, 2014, ANN SCUOLA NORM-SCI, V13, P1065
[14]  
Cianchi A, 1999, J REINE ANGEW MATH, V507, P15
[15]   GLOBAL GRADIENT ESTIMATES IN ELLIPTIC PROBLEMS UNDER MINIMAL DATA AND DOMAIN REGULARITY [J].
Cianchi, Andrea ;
Maz'ya, Vladimir .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2015, 14 (01) :285-311
[16]   Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems [J].
Cianchi, Andrea ;
Maz'ya, Vladimir G. .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 212 (01) :129-177
[17]   Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations [J].
Cianchi, Andrea ;
Maz'ya, Vladimir G. .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (01) :100-133
[18]   Calderon-Zygmund estimates and non-uniformly elliptic operators [J].
Colombo, Maria ;
Mingione, Giuseppe .
JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 270 (04) :1416-1478
[19]   Bounded Minimisers of Double Phase Variational Integrals [J].
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[20]   Regularity for Double Phase Variational Problems [J].
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