PARTIAL REGULARITY FOR ELLIPTIC EQUATIONS

被引：14

作者：

Tian, Guji ^{[1
]}

Wang, Xu-jia ^{[2
]}

机构：

[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China

[2] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 28卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Partial regularity; elliptic equation; perturbation argument; PARTIAL DIFFERENTIAL EQUATIONS; MAXIMUM PRINCIPLE; INTERIOR;

D O I：

10.3934/dcds.2010.28.899

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study partial and anisotropic Schauder estimates for linear and nonlinear elliptic equations. We prove that if the inhomogeneous term f is Holder continuous in the x(n)-direction, then the mixed derivatives u(xxn) are Holder continuous; if f satisfies an anisotropic Holder continuity condition, then the second derivatives D(2)u satisfy related anisotropic Holder continuity estimates.

引用

页码：899 / 913

页数：15

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