Boundary pointwise C1,α and C2,α regularity for fully nonlinear elliptic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Lian, Yuanyuan¹  Zhang, Kai¹ 

[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Shaanxi, Peoples R China

关键词: Boundary regularity;    Schauder estimate;    Fully nonlinear elliptic equation;    Viscosity solution;   

DOI  :  10.1016/j.jde.2020.01.006

来源: Elsevier

【 摘 要 】

In this paper, we obtain the boundary pointwise C-1,C-alpha and C-2,C-alpha regularity for viscosity solutions of fully nonlinear elliptic equations. That is, if partial derivative Omega is C-1,C-alpha(or C-2,C-alpha) at x(0) is an element of partial derivative Omega, the solution is C-1,C-alpha(or C-2,C-alpha) at x(0). Our results are new even for the Laplace equation. Moreover, our proofs are simple. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free