Two-Term Spectral Asymptotics in Linear Elasticity

Matteo Capoferri, Leonid Friedlander, Michael Levitin, Dmitri Vassiliev

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Abstract

We establish the two-term spectral asymptotics for boundary value problems of linear elasticity on a smooth compact Riemannian manifold of arbitrary dimension. We also present some illustrative examples and give a historical overview of the subject. In particular, we correct erroneous results published by Liu (J Geom Anal 31:10164–10193, 2021).
Original languageEnglish
Article number242
JournalJournal of Geometric Analysis
Volume33
Issue number8
Early online date13 May 2023
DOIs
Publication statusPublished - Aug 2023

Keywords

  • 74J05
  • Rayleigh waves
  • Dirichlet conditions
  • Eigenvalue counting function
  • Elasticity
  • Free boundary conditions
  • Primary 35P20
  • Secondary 35Q74

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