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Russian Academy of Sciences. Sbornik. Mathematics, 1995, Volume 81, Issue 1, Pages 101–136
DOI: https://doi.org/10.1070/SM1995v081n01ABEH003617
(Mi sm876)
 

This article is cited in 58 scientific papers (total in 58 papers)

On solvability of nonlocal problems for a second-order elliptic equation

A. K. Gushchina, V. P. Mikhailov

a Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: This article is an investigation of the solvability of nonlocal problems for an elliptic equation, in which the values of the solution on the boundary of the domain $\mathcal{Q}$ under consideration are expressed in terms of its values at interior points and other points of the boundary.
A new concept of solution (in the space of $(n-1)$-dimensionally continuous functions) is introduced, broader than concepts considered previously, and sufficient conditions are established for the problem to be Fredholm with index zero. The connection between solvability of the problem in this formulation and in the classical formulation is studied. In particular, there is a class of nonlocal problems (including some problems studied previously) that are Fredholm with index zero in the formulation introduced but not in the classical formulation (sometimes not even Fredholm). For a certain class of problems a theorem on unique solvability is proved.
Received: 24.06.1993
Russian version:
Matematicheskii Sbornik, 1994, Volume 185, Number 1, Pages 121–160
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: Primary 35J25; Secondary 47A53
Language: English
Original paper language: Russian
Citation: A. K. Gushchin, V. P. Mikhailov, “On solvability of nonlocal problems for a second-order elliptic equation”, Mat. Sb., 185:1 (1994), 121–160; Russian Acad. Sci. Sb. Math., 81:1 (1995), 101–136
Citation in format AMSBIB
\Bibitem{GusMik94}
\by A.~K.~Gushchin, V.~P.~Mikhailov
\paper On solvability of nonlocal problems for a~second-order elliptic equation
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 1
\pages 121--160
\mathnet{http://mi.mathnet.ru/sm876}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1264079}
\zmath{https://zbmath.org/?q=an:0827.35034}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 81
\issue 1
\pages 101--136
\crossref{https://doi.org/10.1070/SM1995v081n01ABEH003617}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995QZ14400007}
Linking options:
  • https://www.mathnet.ru/eng/sm876
  • https://doi.org/10.1070/SM1995v081n01ABEH003617
  • https://www.mathnet.ru/eng/sm/v185/i1/p121
  • This publication is cited in the following 58 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:820
    Russian version PDF:287
    English version PDF:15
    References:82
    First page:4
     
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