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

Serguei A. Nazarov

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 283-292
  • ISSN: 0862-7959

Abstract

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

How to cite

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Nazarov, Serguei A.. "Localization effects for eigenfunctions near to the edge of a thin domain." Mathematica Bohemica 127.2 (2002): 283-292. <http://eudml.org/doc/249067>.

@article{Nazarov2002,
abstract = {It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain $\Omega _h$ is localized either at the whole lateral surface $\Gamma _h$ of the domain, or at a point of $\Gamma _h$, while the eigenfunction decays exponentially inside $\Omega _h$. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.},
author = {Nazarov, Serguei A.},
journal = {Mathematica Bohemica},
keywords = {spectral problem; thin domain; boundary layer; trapped mode; localized eigenfunction; spectrum; thin domain; boundary layer; trapped mode; localized eigenfunction; mixed boundary value problem; Laplacian},
language = {eng},
number = {2},
pages = {283-292},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Localization effects for eigenfunctions near to the edge of a thin domain},
url = {http://eudml.org/doc/249067},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Nazarov, Serguei A.
TI - Localization effects for eigenfunctions near to the edge of a thin domain
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 283
EP - 292
AB - It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain $\Omega _h$ is localized either at the whole lateral surface $\Gamma _h$ of the domain, or at a point of $\Gamma _h$, while the eigenfunction decays exponentially inside $\Omega _h$. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.
LA - eng
KW - spectral problem; thin domain; boundary layer; trapped mode; localized eigenfunction; spectrum; thin domain; boundary layer; trapped mode; localized eigenfunction; mixed boundary value problem; Laplacian
UR - http://eudml.org/doc/249067
ER -

References

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