Gap opening in the essential spectrum of the elasticity theory problem in a periodic half-layer

Nazarov, S.

doi:10.1090/S1061-0022-10-01095-2

Gap opening in the essential spectrum of the elasticity theory problem in a periodic half-layer
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by S. A. Nazarov
Translated by: A. Plotkin

St. Petersburg Math. J. 21 (2010), 281-307

DOI: https://doi.org/10.1090/S1061-0022-10-01095-2

Published electronically: January 26, 2010

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Abstract:

Rayleigh waves are studied in an elastic half-layer with a periodic end and rigidly clamped faces. It is established that the essential spectrum of the corresponding problem of elasticity theory has a band structure, and an example of a waveguide is presented in which a gap opens in the essential spectrum; i.e., an interval arises that contains points of an at most discrete spectrum.

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