Remarks on convexity estimates for solutions of the torsion problem

被引：3

作者：

Jia, Xiaohan ^{[1
]}

Ma, Xi-Nan ^{[2
]}

Shi, Shujun ^{[3
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

[3] Harbin Normal Univ, Sch Math Sci, Harbin 150025, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2023年 / 66卷 / 05期

基金：

中国国家自然科学基金;

关键词：

convexity estimate; superharmonicity; maximum principle; torsion problem; LEVEL SETS;

D O I：

10.1007/s11425-021-1957-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, for the solution of the torsion problem about the equation Delta u = -2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in R-n, we find a superharmonic function which implies the strict concavity of u(1/2) and give some convexity estimates. It is a generalization of Makar-Limanov's result (Makar-Limanov (1971)) and Ma-Shi-Ye's result (Ma et al. (2012)).

引用

页码：1003 / 1020

页数：18

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