Russian Journal of Mathematical Physics

, Volume 15, Issue 2, pp 238–242

On the spectrum of narrow periodic waveguides


DOI: 10.1134/S1061920808020076

Cite this article as:
Friedlander, L. & Solomyak, M. Russ. J. Math. Phys. (2008) 15: 238. doi:10.1134/S1061920808020076


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.

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA
  2. 2.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael