Abstract
We study the asymptotic behavior of the spectrum of the Laplace equation with the Steklov, Dirichlet, Neumann boundary conditions or their combination in a twodimensional domain with small holes of diameter O(e) as e → +0. We derive and justify asymptotic expansions of eigenvalues and eigenfunctions of two types: series in 𝔷 = | ln e|−1 and power series with rational and holomorphic terms in 𝔷 respectively. For the overall Steklov problem we obtain asymptotic expansions in the low and middle frequency ranges of the spectrum. Bibliography: 18 titles.
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