Boundary Lipschitz Regularity of Solutions for Semilinear Elliptic Equations in Divergence Form

被引：0

作者：

Liang, Jing Qi ^{[1
]}

Wang, Li He ^{[1
,2
]}

Zhou, Chun Qin ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, CMA Shanghai, Shanghai 200240, Peoples R China

[2] Univ Iowa, Dept Math, Iowa City, IA USA

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2023年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Boundary Lipschitz regularity; semilinear elliptic equation; Dini condition; Reifenberg domain; DIFFERENTIABILITY; DOMAINS;

D O I：

10.1007/s10114-023-1171-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary. If the domain satisfies C-1,C-Dini condition at a boundary point, and the nonhomogeneous term satisfies Dini continuity condition and Lipschitz Newtonian potential condition, then the solution is Lipschitz continuous at this point. Furthermore, we generalize this result to Reifenberg C-1,C-Dini domains.

引用

页码：193 / 208

页数：16

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