Geodesic
Asymptotic expansions of the eigenvalues of boundary value problems for the Laplace operator in domains with small holes
Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 321-345

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Complete asymptotic expansions are found for the first eigenvalues and eigenfunctions of classical problems for the Laplace operator in two- and three-dimensional domains with small holes. Bibliography: 17 titles. 
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     author = {V. G. Maz'ya and S. A. Nazarov and B. A. Plamenevskii},
     title = {Asymptotic expansions of the eigenvalues of boundary value problems for the {Laplace} operator in domains with small holes},
     journal = {Izvestiya. Mathematics },
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V. G. Maz'ya; S. A. Nazarov; B. A. Plamenevskii. Asymptotic expansions of the eigenvalues of boundary value problems for the Laplace operator in domains with small holes. Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 321-345. http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a5/