, Volume 15, Issue 2, pp 238-242
Date: 11 Jun 2008

On the spectrum of narrow periodic waveguides

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Abstract

This is a continuation of [1] and [2]. We consider the spectrum of the Dirichlet Laplacian on the domain {(x, y) : 0 < y < εh(x)}, where h(x) is a positive periodic function. The main assumption is that h(x) has one point of global maximum on the period interval. We study the location of bands and prove that the band lengths decay exponentially as ε → 0.

To the memory of Leonid Romanovich Volevich