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Mathematics of the USSR-Sbornik, 1976, Volume 28, Issue 4, Pages 459–480
DOI: https://doi.org/10.1070/SM1976v028n04ABEH001663 (Mi sm2770) 		 
This article is cited in 61 scientific papers (total in 63 papers)

A boundary value problem for the elliptic equation of second order in a domain with a narrow slit. 1. The two-dimensional case

A. M. Il'in
English version PDF (1557 kB) Citations (63) Russian version article
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DOI: https://doi.org/10.1070/SM1976v028n04ABEH001663
Abstract: An elliptic equation is considered in a domain $D_\varepsilon$ that is obtained from a two-dimensional domain $D$ by removing a neighborhood of a segment. It is assumed that this neighborhood contracts to the segment as $\varepsilon\to0$. An asymptotic expansion of the solution of the first boundary value problem in $D_\varepsilon$ is constructed and justified.
Bibliography: 5 titles.
Received: 02.09.1975
Bibliographic databases:
UDC: 517.946
MSC: 35J25, 35B40
Language: English
Original paper language: Russian
Citation: A. M. Il'in, “A boundary value problem for the elliptic equation of second order in a domain with a narrow slit. 1. The two-dimensional case”, Math. USSR-Sb., 28:4 (1976), 459–480
Citation in format AMSBIB
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\by A.~M.~Il'in
\paper A~boundary value problem for the elliptic equation of second order in a~domain with a~narrow slit. 1.~The two-dimensional case
\jour Math. USSR-Sb.
\yr 1976
\vol 28
\issue 4
\pages 459--480
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\crossref{https://doi.org/10.1070/SM1976v028n04ABEH001663}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=407439}
\zmath{https://zbmath.org/?q=an:0333.35033}
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  • https://www.mathnet.ru/eng/sm/v141/i4/p514
    Cycle of papers
    This publication is cited in the following 63 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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