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Mat. Sb. (N.S.), 1973, Volume 91(133), Number 4(8), Pages 488–499 (Mi msb3311)  

This article is cited in 2 scientific papers (total in 2 papers)

On the approximation of solutions of boundary value problems in domains with an unbounded boundary

L. Shimon


Abstract: Elliptic problems with a complex parameter $q$ are considered for equations with variable coefficients in domains $\Omega$ with an unbounded boundary. It is proved that for sufficiently large $|q|$ the problem has a unique solution in the space $H^s(\Omega)$ and that the solution can be obtained as the limit as $r\to\infty$ of the solution of a boundary value problem in a certain bounded domain $\Omega_r\subset\Omega$.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 20:4, 506–518

Bibliographic databases:

UDC: 517.946.9
MSC: Primary 35J40, 35A35; Secondary 35B45
Received: 13.09.1972

Citation: L. Shimon, “On the approximation of solutions of boundary value problems in domains with an unbounded boundary”, Mat. Sb. (N.S.), 91(133):4(8) (1973), 488–499; Math. USSR-Sb., 20:4 (1973), 506–518

Citation in format AMSBIB
\Bibitem{Shi73}
\by L.~Shimon
\paper On~the approximation of solutions of boundary value problems in domains with an unbounded boundary
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 4(8)
\pages 488--499
\mathnet{http://mi.mathnet.ru/msb3311}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=330761}
\zmath{https://zbmath.org/?q=an:0277.35044}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 4
\pages 506--518
\crossref{https://doi.org/10.1070/SM1973v020n04ABEH001887}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Ya. Spiridonov, “Approximation of solutions of elliptic problems in domains with noncompact boundaries by solutions of exterior or interior problems”, Math. USSR-Sb., 53:2 (1986), 551–561  mathnet  crossref  mathscinet  zmath
    2. V. S. Rabinovich, “Stability of the Inverse Operators of Boundary Value Problems in Smooth Expanding Domains”, Funct. Anal. Appl., 35:4 (2001), 309–311  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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