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(ε) as ε → +0. We derive and justify asymptotic expansions of eigenvalues and eigenfunctions of two types: series in ʓ= | ln ε|−1 and power series with rational and holomorphic terms in ʓ respectively. For the overall Steklov problem we obtain asymptotic expansions in the low and middle frequency ranges of the spectrum. Bibliography: 18 titles.
Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition / Chiado' Piat, V.; Nazarov, S. A.. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - 251:5(2020), pp. 655-695. [10.1007/s10958-020-05122-3]
Titolo: | Mixed Boundary Value Problems in Singularly Perturbed Two-Dimensional Domains with the Steklov Spectral Condition | |
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Data di pubblicazione: | 2020 | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10958-020-05122-3 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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Na_2D_2019corr.pdf | 2. Post-print / Author's Accepted Manuscript | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2862085