On the Spectrum of the Dirichlet Laplacian in a Narrow Strip

2007/05/28 by Leonid Friedlander, Michael Solomyak, Friedlander, Leonid +1 · 6 citations
Mathematics · Computer Science · Materials Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.0705.4058

Abstract

We derive a two-terms asymptotics for eigenvalues of the Dirichlet Laplacian in a narrow strip of variable width. The asymptotics is taken with respect to a small paprameter that characterizes the width of the strip.

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• Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in R^d
• Eigenvalue falls in thin broken quantum strips
• Cauchy Data for 1D singular Schrödinger operators
• Homogenization of an indefinite spectral problem arising in population genetics

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