Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions

Title:

Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions

Creator:

Krejčiřík, David

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:56dec050-bff0-46c4-a6d3-2f430be88aba
uuid:56dec050-bff0-46c4-a6d3-2f430be88aba
doi:10.21136/MB.2014.143848

Subject:

Laplacian in tubes, Dirichlet boundary condition, Neumann boundary condition, eigenvalue asymptotics, dimension reduction, quantum waveguides, and mean curvature

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the area of the Neumann boundary to the Dirichlet one is locally the biggest.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

185-193

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false