An example of multiple gaps in the spectrum of a~periodic waveguide
Sbornik. Mathematics, Tome 201 (2010) no. 4, pp. 569-594
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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.
Keywords:
gaps in the essential spectrum, formally self-adjoint elliptic system of differential equations with polynomial property.
@article{SM_2010_201_4_a3,
author = {S. A. Nazarov},
title = {An example of multiple gaps in the spectrum of a~periodic waveguide},
journal = {Sbornik. Mathematics},
pages = {569--594},
publisher = {mathdoc},
volume = {201},
number = {4},
year = {2010},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2010_201_4_a3/}
}
S. A. Nazarov. An example of multiple gaps in the spectrum of a~periodic waveguide. Sbornik. Mathematics, Tome 201 (2010) no. 4, pp. 569-594. http://geodesic.mathdoc.fr/item/SM_2010_201_4_a3/