C1,α regularity of solutions of some degenerate fully non-linear elliptic equations

被引：71

作者：

Imbert, C. ^{[2
,3
]}

Silvestre, L. ^{[1
]}

机构：

[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[2] Univ Paris Est Creteil Val de Marne, CNRS, UMR 8050, F-94010 Creteil, France

[3] Univ Paris Est Creteil Val de Marne, Lab Analyse & Math Appl, F-94010 Creteil, France

来源：

ADVANCES IN MATHEMATICS | 2013年 / 233卷 / 01期

基金：

美国国家科学基金会;

关键词：

C-1; C-alpha estimates; Degenerate elliptic equations; Fully non-linear elliptic equations; Viscosity solutions; VISCOSITY SOLUTIONS; EIGENVALUE; OPERATORS;

D O I：

10.1016/j.aim.2012.07.033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, a class of fully non-linear elliptic equations are considered, which are degenerate as the gradient becomes small. Holder estimates obtained by the first author (2011) are combined with new Lipschitz estimates obtained through the Ishii-Lions method in order to get C-1,C-alpha estimates for solutions of these equations. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：196 / 206

页数：11

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