Concavity of solutions to semilinear equations in dimension two

被引：1

作者：

Chau, Albert ^{[1
]}

Weinkove, Ben ^{[2
]}

机构：

[1] Univ British Columbia, Dept Math, 1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

[2] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2023年 / 55卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

CONVEX SOLUTIONS; POWER CONCAVITY; LEVEL SETS;

D O I：

10.1112/blms.12750

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Dirichlet problem for a class of semilinear equations on two- dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions.

引用

页码：706 / 716

页数：11

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