Some applications of pseudo-differential operators to elasticity

Alexander Kozhevnikov, Tatiana Skubachevskaya

Research output: Contribution to journalArticlepeer-review


The paper deals with four basic boundary value problem of static elasticity (BPET). It was calculated the principal symbol of a pseudo-differential operator on the boundary whose eigenvalues are the Cosserat eigenvalues of the original BPET. This principal symbol is presented in terms of the principal curvatures and the coefficients of the first quadratic form of the boundary. It was found the principal term in the asympotics of the Cosserat eigenvalues.

Original languageEnglish
Pages (from-to)297-322
Number of pages26
JournalHokkaido Mathematical Journal
Issue number2
StatePublished - 1997


  • Asymptotics
  • Boundary value problems
  • Cosserat spectrum
  • Elasticity
  • Isotropic and homogeneous elastic body
  • Lamé equation
  • Poisson constant
  • Principal symbol
  • Pseudo-differential operators

ASJC Scopus subject areas

  • General Mathematics


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