A Rigidity Result for the Robin Torsion Problem

被引：4

作者：

Masiello, Alba Lia ^{[1
]}

Paoli, Gloria ^{[2
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicazioni Renato Cacciop, Via Cintia, I-80126 Naples, Italy

[2] Chair Dynam Control & Numer Alexander Humboldt Pro, Dept Data Sci DDS, Cauerstr 11, D-91058 Erlangen, Germany

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 05期

关键词：

Robin boundary conditions; Laplace operator; Rigidity result; Torsion problem; Talenti comparison; ELLIPTIC PROBLEMS; REARRANGEMENTS; EQUATIONS;

D O I：

10.1007/s12220-023-01202-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let omega subset of R-2 be an open, bounded and Lipschitz set. We consider the torsion problem for the Laplace operator associated to Q with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison, proved in Alvino et al. (Commun Pure Appl Math 76:585-603, 2023).. We prove that the equality is achieved only if omega is a disk and the torsion function u is radial.

引用

页数：14

共 24 条

[1] Sharp estimates for solutions to elliptic problems with mixed boundary conditions [J].