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Mat. Sb. (N.S.), 1983, Volume 120(162), Number 3, Pages 291–310 (Mi msb2131)  

This article is cited in 5 scientific papers (total in 5 papers)

On certain generalizations of the Dirichlet problem

Yu. A. Rozanov


Abstract: A characterization is given of boundary conditions for linear differential operators in a domain with arbitrary boundary, and these conditions are used to state a boundary-value problem in a suitable function class. It is proved that this “generalized Dirichlet problem” has a unique solution which depends continuously on the boundary conditions.
Bibliography: 3 titles.

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English version:
Mathematics of the USSR-Sbornik, 1984, 48:2, 287–305

Bibliographic databases:

UDC: 517.544
MSC: Primary 35A05, 35D05, 35G15, 35B30; Secondary 31B20, 46E35, 44F05, 60G60, 60J99
Received: 22.04.1982

Citation: Yu. A. Rozanov, “On certain generalizations of the Dirichlet problem”, Mat. Sb. (N.S.), 120(162):3 (1983), 291–310; Math. USSR-Sb., 48:2 (1984), 287–305

Citation in format AMSBIB
\Bibitem{Roz83}
\by Yu.~A.~Rozanov
\paper On certain generalizations of the Dirichlet problem
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 120(162)
\issue 3
\pages 291--310
\mathnet{http://mi.mathnet.ru/msb2131}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=691979}
\zmath{https://zbmath.org/?q=an:0574.60067}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 287--305
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002675}


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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. V. A. Bulychev, “The Markov Property of an Evolutionary Stochastic Equation”, Theory Probab Appl, 31:2 (1987), 322  mathnet  crossref  mathscinet  zmath  isi
    2. V. A. Bulychev, F. F. Frolov, “Boundary value problems for generalized differential equations”, Math. USSR-Sb., 63:2 (1989), 267–287  mathnet  crossref  mathscinet  zmath
    3. Arato N., “Quadratic Functionals of Generalized Gaussian Random-Fields”, Comput. Math. Appl., 19:1 (1990), 1–7  crossref  mathscinet  zmath  isi
    4. Arato N., “Limit Boundary-Value-Problems in Regions with Random Fine-Grained Boundaries”, Appl. Math. Lett., 8:4 (1995), 1–6  crossref  mathscinet  zmath  isi
    5. A. K. Gushchin, “Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation”, Sb. Math., 189:7 (1998), 1009–1045  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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