On the spectrum of narrow periodic waveguides

Leonid Friedlander, M. Solomyak

Research output: Contribution to journalArticle

32 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)238-242
Number of pages5
JournalRussian Journal of Mathematical Physics
Volume15
Issue number2
DOIs
Publication statusPublished - Jun 2008

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ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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