INTERIOR C1,α REGULARITY OF WEAK SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS

被引：0

作者：

Yao, Fengping ^{[1
]}

Zhou, Shulin ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 05期

关键词：

C-1; C-alpha regularity; divergence; quasilinear; elliptic; HOLDER;

D O I：

10.3934/dcdsb.2016015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a new proof for the interior C-1,C-alpha regularity of weak solutions for a class of quasilinear elliptic equations, whose prototype is the p-Laplace equation.

引用

页码：1635 / 1649

页数：15

共 20 条

[1]

[Anonymous], 2015, Elliptic Partial Differential Equations of Second Order. Classics in Mathematics

[2]

[Anonymous], 2003, SOBOLEV SPACES

[3]

[Anonymous], 1983, MULTIPLE INTEGRALS C

[4] Gradient estimates in Orlicz space for nonlinear elliptic equations [J].

Byun, Sun-Sig ;

Yao, Fengping ;

Zhou, Shulin .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (08) :1851-1873

[5] INTERIOR A PRIORI ESTIMATES FOR SOLUTIONS OF FULLY NON-LINEAR EQUATIONS [J].

CAFFARELLI, LA .

ANNALS OF MATHEMATICS, 1989, 130 (01) :189-213

[6]

CHEN Y, 1998, 2 ORDER ELLIPTIC PAR

[7] 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

[8] C1+ALPHA LOCAL REGULARITY OF WEAK SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

DIBENEDETTO, E .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (08) :827-850

[9] Local Lipschitz regularity for degenerate elliptic systems [J].

Duzaar, Frank ;

Mingione, Giuseppe .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (06) :1361-1396

[10] Gradient estimates via linear and nonlinear potentials [J].

Duzaar, Frank ;

Mingione, Giuseppe .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (11) :2961-2998

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