Displaying similar documents to “Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains”

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

Serguei A. Nazarov (2002)

Mathematica Bohemica

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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.