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)).
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页码：1003 / 1020
页数：18
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