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Siberian Mathematical Journal

, Volume 54, Issue 3, pp 517–532 | Cite as

The localization for eigenfunctions of the dirichlet problem in thin polyhedra near the vertices

  • S. A. NazarovEmail author
Article

Abstract

Under some geometric assumptions, we show that eigenfunctions of the Dirichlet problem for the Laplace operator in an n-dimensional thin polyhedron localize near one of its vertices. We construct and justify asymptotics for the eigenvalues and eigenfunctions. For waveguides, which are thin layers between periodic polyhedral surfaces, we establish the presence of gaps and find asymptotics for their geometric characteristics.

Keywords

Dirichlet problem asymptotics of spectrum localization of eigenfunctions spectral gaps 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Institute of Problems of Mechanical EngineeringSt. Petersburg State UniversitySt. PetersburgRussia

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