An example of multiple gaps in the spectrum of a periodic waveguide

S. A. Nazarov

Sbornik. Mathematics, Tome 201 (2010) no. 4, pp. 569-594

Résumé

A periodic waveguide is constructed, whose shape depends on a small parameter $h>0$, in which the essential spectrum of the operators for some boundary-value problems (Dirichlet, Neumann, and mixed under certain restrictions) for a formally self-adjoint elliptic system of second-order differential equations acquires any pre-assigned number of gaps. The geometric shape of the waveguide can be interpreted as an infinite periodic set of beads connected by thin, short ligaments. The proof of that gaps appear is based on an application of the max-min principle and the weighted Korn inequality. Bibliography: 43 titles.

Détail

Keywords: gaps in the essential spectrum, formally self-adjoint elliptic system of differential equations with polynomial property.

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