Y. Amirat, G. A. Chechkin, R. R. Gadyl'shin, “Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary”, Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 1,Pages <nobr>102

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

Y. Amirat^a, G. A. Chechkin^b, R. R. Gadyl'shin^cd

^a Laboratoire de Mathématiques, Université Blaise Pascal, CNRS UMR 6620, 63177 Aubière cedex, France
^b Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia
^c Department of Mathematical Analysis, Faculty of Physics and Mathematics, Bashkir State Pedagogical University, Ufa, 450000, Russia
^d Institute of Mathematics (with Computing Center), Russian Academy of Sciences, Ufa, 450077, Russia

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.

Key words: oscillating boundary, spectrum of the Laplacian, asymptotics, matching of asymptotic expansions.

UDC: 519.632.4

Received: 07.06.2005

Language: English