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The asymptotics of the solution to the Neumann spectral problem in a domain of the “dense-comb” type

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Abstract

Convergence theorems and asymptotic estimates (as ε → 0) are proved for the eigenvalues and the eigenfunctions of the Neumann problem in a dense singular junction Ω ɛ of a domain Ω0 and a large number N of thin cylinders with thickness of order ε=lN−1, where l is the total length of common boundaries for Ω0 and the cylinders in question. Bibliography: 27 titles.

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We dedicate the present paper to Olga Arsenievna Oleinik, as a symbol of our deep respect and gratitude

Translated from Trudy Seminara imeni I G. Petrovskogo, No. 19. pp. 000-000. 0000.

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Melnik, T.A., Nazarov, S.A. The asymptotics of the solution to the Neumann spectral problem in a domain of the “dense-comb” type. J Math Sci 85, 2326–2346 (1997). https://doi.org/10.1007/BF02355841

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  • DOI: https://doi.org/10.1007/BF02355841

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