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Asymptotic expansions of the eigenvalues and eigenfunctions of an elliptic operator in a domain with many ”light” concentrated masses near the boundary. The two-dimensional case. (English. Russian original) Zbl 1102.35035
Izv. Math. 69, No. 4, 805-846 (2005); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 69, No. 4, 161-204 (2005).
The author considers the vibrations of a membrane which contains many ”light” periodically situated masses. Using the method of matching of asymptotic expansions he constructs complete asymptotic expansions of the eigenvalues and eigenfunctions and give a justification of such expansions

MSC:
35J25 Boundary value problems for second-order elliptic equations
35B25 Singular perturbations in context of PDEs
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
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