Eigenvalues of the Laplacian in a Disk with the Dirichlet Condition on Finitely Many Small Boundary Parts in the Critical Case

被引：0

作者：

Gadyl’shin R.R. ^{[1
,2
]}

Rep’evskii S.V. ^{[3
]}

Shishkina E.A. ^{[1
]}

机构：

[1] M. Akmullah Bashkir State Pedagogical University, 3a, Oktyabrskoy Revolutsii St., Ufa

[2] Bashkir State University, 32, Frunze st., Ufa

[3] Chelyabinsk State University, 129, Brat’ev Kashirinykh St., Chelyabinsk

来源：

Journal of Mathematical Sciences | 2016年 / 213卷 / 4期

关键词：

Asymptotic Expansion; Dirichlet Boundary Condition; Critical Case; Internal Expansion; Matched Asymptotic Expansion;

D O I：

10.1007/s10958-016-2722-4

中图分类号：

学科分类号：

摘要：

We consider the boundary value problem for eigenvalues of the negative Laplace operator in a disk with the Neumann boundary condition on the circle except for finitely many (more than 1) small arcs, where the Dirichlet boundary condition is imposed, with lengths tending to zero. We construct complete asymptotics expansions of egenvalues with respect to the parameter (the arc length) converging to a double eigenvalue to the limit Neumann problem, in the critical case, where one of the eigenfunctions of the limit problem vanishes at all contraction points for small arcs. © 2016, Springer Science+Business Media New York.

引用

页码：510 / 529

页数：19

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