A gap in the continuous spectrum of a cylindrical waveguide with a periodic perturbation of the surface

Abstract

It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the continuous spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the cylinder are small, the gap certainly opens.

arXiv comment24 pages, 9 figures

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