Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with an oscillating boundary

  • Y. Amirat
  • G. A. Chechkin
  • R. R. Gadyl’shin
Article

Abstract

The asymptotic behavior of solutions to spectral problems for the Laplace operator in a domain with a rapidly oscillating boundary is analyzed. The leading terms of the asymptotic expansions for eigenelements are constructed, and the asymptotics are substantiated for simple eigenvalues.

Keywords

oscillating boundary spectrum of the Laplacian asymptotics matching of asymptotic expansions 

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Copyright information

© MAIK “Nauka/Interperiodica” 2006

Authors and Affiliations

  • Y. Amirat
    • 1
  • G. A. Chechkin
    • 2
  • R. R. Gadyl’shin
    • 3
    • 4
  1. 1.Laboratoire de MathématiquesUniversité Blaise PascalAubière cedexFrance
  2. 2.Department of Differential Equations, Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  3. 3.Institute of Mathematics (with Computing Center)Russian Academy of SciencesUfaRussia
  4. 4.Department of Mathematical Analysis, Faculty of Physics and MathematicsBashkir State Pedagogical UniversityUfaRussia

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