Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps

Abstract

We construct a family of periodic elastic waveguides Π _h , depending on a small geometrical parameter, with the following property: as h → +0, the number of gaps in the essential spectrum of the elasticity system on Π _h grows unboundedly.

Keywords:

• linear elasticity system
• periodic waveguide
• spectral gap

AMS Subject Classifications::

• Primary 35J20
• Secondary 35P99

Acknowledgements

The first author was partially supported by the Academy of Finland grant no. 127245 and by RFFI, grant 09-01-00759. The third author was partially supported by the Väisälä Foundation of the Finnish Academy of Science and Letters.