Overdetermined elliptic problems in topological disks

被引：3

作者：

Mira, Pablo ^{[1
]}

机构：

[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Cartagena, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 11期

关键词：

CONSTANT MEAN-CURVATURE; HYPERSURFACES; CONJECTURE; SYMMETRY; PLANE;

D O I：

10.1016/j.jde.2018.02.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a method, based on the Poincare-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：6994 / 7005

页数：12

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