On an Eigenvalue for the Laplace Operator in a Disk with Dirichlet Boundary Condition on a Small Part of the Boundary in a Critical Case

被引：1

作者：

Gadyl'shin, R. R. ^{[1
]}

Rep'evskii, S. V. ^{[2
]}

Shishkina, E. A. ^{[1
]}

机构：

[1] Bashkir State Pedag Univ, Ul Oktyabrskoi Revolyutsii 3A, Ufa 450000, Russia

[2] Chelyabinsk State Univ, Ul Br Kashirinykh 129, Chelyabinsk 454001, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2016年 / 292卷

基金：

俄罗斯基础研究基金会;

关键词：

Laplace operator; singular perturbation; small parameter; eigenvalue; asymptotics;

D O I：

10.1134/S0081543816020073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A boundary-value problem of finding eigenvalues is considered for the negative Laplace operator in a disk with Neumann boundary condition on almost all the circle except for a small arc of vanishing length, where the Dirichlet boundary condition is imposed. A complete asymptotic expansion with respect to a parameter (the length of the small arc) is constructed for an eigenvalue of this problem that converges to a double eigenvalue of the Neumann problem.

引用

页码：S76 / S90

页数：15

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