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Izvestiya: Mathematics, 2005, Volume 69, Issue 4, Pages 805–846
DOI: https://doi.org/10.1070/IM2005v069n04ABEH001665 (Mi im652) 		 
This article is cited in 31 scientific papers (total in 31 papers)

Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many “light” concentrated masses situated on the boundary. Two-dimensional case

G. A. Chechkin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (446 kB) Citations (31)
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DOI: https://doi.org/10.1070/IM2005v069n04ABEH001665
Abstract: We consider vibrations of a membrane which contains many “light” concentrated masses on the boundary. We study the asymptotic behaviour of the frequencies of eigenvibrations of the membrane as the small parameter (which characterizes the diameter and density of the concentrated masses) tends to zero. We construct asymptotic expansions of eigenelements of the corresponding problems and carefully justify these expansions.
Received: 02.06.2004
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2005, Volume 69, Issue 4, Pages 161–204
DOI: https://doi.org/10.4213/im652
Bibliographic databases:
UDC: 517.956.226
MSC: 35J25, 35B25, 35B27, 35B40
Language: English
Original paper language: Russian
Citation: G. A. Chechkin, “Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many “light” concentrated masses situated on the boundary. Two-dimensional case”, Izv. RAN. Ser. Mat., 69:4 (2005), 161–204; Izv. Math., 69:4 (2005), 805–846
Citation in format AMSBIB
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    English version PDF:7
    References:100
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