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.
A gap in the essential spectrum of a cylindrical waveguide with a periodic perturbation of the surface / Cardone, G; Nazarov, Sa; Perugia, C. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 283:9(2010), pp. 1222-1244. [10.1002/mana.200910025]
A gap in the essential spectrum of a cylindrical waveguide with a periodic perturbation of the surface
Cardone G
;Perugia C
2010
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.File in questo prodotto:
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