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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.
Fuente: Transactions of the American Mathematical Society 368 (2016), 4787-4829
Publisher: American Mathematical Society
Publication date: 01/07/2016
No. of pages: 43
Publication type: Article
DOI: 10.1090/tran/6625
ISSN: 0002-9947,1088-6850
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NAZAROV, SERGEI A.
MARIA EUGENIA PEREZ MARTINEZ
TASKINEN, JARI
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