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

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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.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Blaise Pascal, CNRS UMR 6620, 63177, Aubière cedex, France

    Y. Amirat

  2. Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia

    G. A. Chechkin

  3. Institute of Mathematics (with Computing Center), Russian Academy of Sciences, Ufa, 450077, Russia

    R. R. Gadyl’shin

  4. Department of Mathematical Analysis, Faculty of Physics and Mathematics, Bashkir State Pedagogical University, Ufa, 450000, Russia

    R. R. Gadyl’shin

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  1. Y. Amirat
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  2. G. A. Chechkin
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  3. R. R. Gadyl’shin
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Amirat, Y., Chechkin, G.A. & Gadyl’shin, R.R. Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with an oscillating boundary. Comput. Math. and Math. Phys. 46, 97–110 (2006). https://doi.org/10.1134/S0965542506010118

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