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

Y. Amirat   ; G. A. Chechkin   ; R. R. Gadyl'shin

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 1, pp. 102-115

Résumé

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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