A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide

Details A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide

2011-10-27

arxiv.org/abs/1110.5990v1

Mathematics

Spectral Theory

26 pages, 6 figures

Scientific paper

We will study the spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with contains periodic arrangement of inclusions. On the boundary of the waveguide we consider both Neumann and Dirichlet conditions. We will prove that provided the diameter of the inclusion is small enough in the spectrum of Laplacian opens spectral gaps, i.e. frequencies that does not propagate through the waveguide. The existence of the band gaps will verified using the asymptotic analysis of elliptic operators.

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