Localization effects for eigenfunctions near to the edge of a thin domain

Title:

Localization effects for eigenfunctions near to the edge of a thin domain

Creator:

Nazarov, Serguei A.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8e58ff5e-a7c5-4d26-a135-ba3a247938f3
uuid:8e58ff5e-a7c5-4d26-a135-ba3a247938f3
doi:10.21136/MB.2002.134169

Subject:

spectral problem, thin domain, boundary layer, trapped mode, and localized eigenfunction

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain Ωh is localized either at the whole lateral surface Γh of the domain, or at a point of Γh, while the eigenfunction decays exponentially inside Ωh. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.

Language:

English

Rights:

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

Coverage:

283-292

Source:

Mathematica bohemica | 2002 Volume:127 | Number:2

Harvested from:

CDK

Metadata only:

false