Asymptotic behaviour of the Steklov spectrum on dumbbell domains

被引：4

作者：

Bucur, Dorin ^{[1
]}

Henrot, Antoine ^{[2
]}

Michetti, Marco ^{[2
]}

机构：

[1] Univ Savoie Mt Blanc, LAMA, CNRS, Chambery, France

[2] Univ Lorraine, Inst Elie Cartan Lorraine, CNRS UMR 7502, Vandoeuvre Les Nancy, France

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 46卷 / 02期

关键词：

Asymptotic behaviour; dumbbell; Steklov eigenvalues; EIGENVALUES;

D O I：

10.1080/03605302.2020.1840587

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyse the asymptotic behaviour of the eigenvalues and eigenvectors of a Steklov problem in a dumbbell domain consisting of two Lipschitz sets connected by a thin tube with vanishing width. All the eigenvalues are collapsing to zero, the speed being driven by some power of the width which multiplies the eigenvalues of a one dimensional problem. In two dimensions of the space, the behaviour is fundamentally different from the third or higher dimensions and the limit problems are of different nature. This phenomenon is due to the fact that only in dimension two the boundary of the tube has not vanishing surface measure.

引用

页码：362 / 393

页数：32

共 32 条

[1]

[Anonymous], 1988, J FS U TOKYO IA

[2] NEUMANN EIGENVALUE PROBLEMS ON EXTERIOR PERTURBATIONS OF THE DOMAIN [J].