A priori estimates for classical solutions of fully nonlinear elliptic equations

被引：0

作者：

CAO Yi LI DongSheng WANG LiHe College of Science Xian Jiaotong University Xian ChinaDepartment of Mathematics The University of Iowa Iowa City IA USA ^{[1
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机构：

来源：

Science China(Mathematics) | 2011年 / 54卷 / 03期

关键词：

fully nonlinear; classical solutions; C2; α; estimates;

D O I：

暂无

中图分类号：

O175.25 [椭圆型方程];

学科分类号：

070104 ;

摘要：

For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α 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 C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u.

引用

页码：457 / 462

页数：6