Boundary Lipschitz Regularity and the Hopf Lemma for Fully Nonlinear Elliptic Equations

被引：1

作者：

Lian, Yuanyuan ^{[1
]}

Zhang, Kai ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai, Peoples R China

来源：

POTENTIAL ANALYSIS | 2024年 / 60卷 / 03期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Boundary regularity; Lipschitz continuity; Hopf lemma; Fully nonlinear elliptic equation; VISCOSITY SOLUTIONS;

D O I：

10.1007/s11118-023-10085-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the boundary regularity for viscosity solutions of fully nonlinear elliptic equations. We use a unified, simple method to prove that if the domain O satisfies the exterior C(1,Dini )condition at x(0) ? ?O, the solution is Lipschitz continuous at x(0); if O satisfies the interior C-1,C-Dini condition at x(0), the Hopf lemma holds at x(0). The key idea is that the curved boundaries are regarded as perturbations of a hyperplane. Moreover, we show that the C-1,C-Dini conditions are optimal.

引用

页码：1231 / 1247

页数：17

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