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Localization effect for Dirichlet eigenfunctions in thin non-smooth domains

Abstract: We study the localization effect for the eigenfunctions of the Laplace-Dirichlet problem in a thin three-dimensional plate with curved non-smooth bases. We show that the eigenfunctions are localized at the thickest region, or the longest traverse axis, of the plate and that the magnitude of the eigenfunctions decays exponentially as a function of the distance to this axis. We consider some extensions like mixed boundary value problems in thin domains. The obtained asymptotic formulas for eigenfunctions prove the existence of gaps in the essential spectrum of the Dirichlet Laplacian in an unbounded double-periodic curved piecewise smooth thin layer.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Transactions of the American Mathematical Society 368 (2016), 4787-4829

Editorial: American Mathematical Society

 Fecha de publicación: 01/07/2016

Nº de páginas: 43

Tipo de publicación: Artículo de Revista

 DOI: 10.1090/tran/6625

ISSN: 0002-9947,1088-6850