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Russian Journal of Mathematical Physics

, Volume 25, Issue 1, pp 73–87 | Cite as

Spectrum of a Problem of Elasticity Theory in the Union of Several Infinite Layers

  • S. A. NazarovEmail author
Article
  • 22 Downloads

Abstract

The essential spectrum of the Dirichlet problem for the system of Lamé equations in a three-dimensional domain formed by three mutually perpendicular elastic layers occupies the ray [Λ,+∞). The lower bound Λ > 0 is the least eigenvalue (its existence is established) of the problem of elasticity theory in an infinite two-dimensional cross-shaped waveguide. It is proved that the discrete spectrum of the spatial problem is nonempty. Other configurations of layers and the scalar problem of the junction of quantum waveguides are also considered.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Mathematics and Mechanics FacultySt. Petersurg State UniversitySt. PetersburgRussia
  2. 2.Peter the Great St. Petersburg State Polytechnic UniversitySt. PetersburgRussia
  3. 3.Institute of Problems of Mechanical Engineering of the Russian Academy of SciencesSt. PetersburgRussia

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