Geodesic
Localization effects for eigenfunctions near to the edge of a thin domain
Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 283-292.

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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.
DOI : 10.21136/MB.2002.134169
Classification : 35B40, 35J25, 35P05, 74B05, 74E10, 74G10
Keywords: spectral problem; thin domain; boundary layer; trapped mode; localized eigenfunction 
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Nazarov, Serguei A. Localization effects for eigenfunctions near to the edge of a thin domain. Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 283-292. doi : 10.21136/MB.2002.134169. http://geodesic.mathdoc.fr/articles/10.21136/MB.2002.134169/

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