Partial regularity of solutions of fully nonlinear, uniformly elliptic equations

被引：30

作者：

Armstrong, Scott N. ^{[1
]}

Silvestre, Luis E. ^{[1
]}

Smart, Charles K. ^{[2
]}

机构：

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

[2] NYU, Courant Inst, New York, NY 10012 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2012年 / 65卷 / 08期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1002/cpa.21394

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is C2,a on the complement of a closed set of Hausdorff dimension at most ? less than the dimension. The equation is assumed to be C1, and the constant ? > 0 depends only on the dimension and the ellipticity constants. The argument combines the W2,? estimates of Lin with a result of Savin on the C2,a regularity of viscosity solutions that are close to quadratic polynomials. (c) 2012 Wiley Periodicals, Inc.

引用

页码：1169 / 1184

页数：16

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