A priori estimates for classical solutions of fully nonlinear elliptic equations

被引：1

作者：

Cao Yi ^{[1
]}

Li DongSheng ^{[1
]}

Wang LiHe ^{[1
,2
]}

机构：

[1] Xi An Jiao Tong Univ, Coll Sci, Xian 710049, Peoples R China

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 03期

基金：

中国国家自然科学基金;

关键词：

fully nonlinear; classical solutions; C-2; C-alpha estimates; INTERIOR;

D O I：

10.1007/s11425-010-4092-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the fully nonlinear uniformly elliptic equation F(D (2) u) = 0, it is well known that the viscosity solutions are C (2,alpha) if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C (1,beta) a.e. for any 0 < beta < 1. We will prove that the classical solutions u are C (2,alpha) . Moreover, the C (2,alpha) norm of u depends on n, F and the continuous modulus of D (2) u.

引用

页码：457 / 462

页数：6

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