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Mat. Sb., 1989, Volume 180, Number 9, Pages 1211–1233 (Mi msb1657)  

This article is cited in 8 scientific papers (total in 8 papers)

On an integral equation for the Dirichlet problem in a plane domain with cusps on the boundary

V. G. Maz'ya, A. A. Soloviev


Abstract: Integral equations for the Dirichlet problem for the Laplace operator are studied in a plane domain whose boundary has interior or exterior peaks with tangency of first order. Theorems on unique solvability and asymptotics of solutions near the peaks are presented.
Bibliography: 8 titles.

Full text: PDF file (990 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1991, 68:1, 61–83

Bibliographic databases:

UDC: 539.3
MSC: 31A25, 35J05, 45A05
Received: 19.09.1988

Citation: V. G. Maz'ya, A. A. Soloviev, “On an integral equation for the Dirichlet problem in a plane domain with cusps on the boundary”, Mat. Sb., 180:9 (1989), 1211–1233; Math. USSR-Sb., 68:1 (1991), 61–83

Citation in format AMSBIB
\Bibitem{MazSol89}
\by V.~G.~Maz'ya, A.~A.~Soloviev
\paper On an integral equation for the Dirichlet problem in a~plane domain with cusps on the boundary
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 9
\pages 1211--1233
\mathnet{http://mi.mathnet.ru/msb1657}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1017822}
\zmath{https://zbmath.org/?q=an:0683.45002|0709.45010}
\transl
\jour Math. USSR-Sb.
\yr 1991
\vol 68
\issue 1
\pages 61--83
\crossref{https://doi.org/10.1070/SM1991v068n01ABEH001196}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991EX22700004}


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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. R. Duduchava, T. Latsabidze, A. Saginashvili, “Singular integral operators with the complex conjugation on curves with cusps”, Integr equ oper theory, 22:1 (1995), 1  crossref  mathscinet  zmath  isi
    2. A. A. Soloviev, “Integral equations for the Dirichlet and Neumann boundary value problems in a plane domain with a cusp on the boundary”, Math. Notes, 59:6 (1996), 637–645  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Chkadua O., “The Dirichlet, Neumann and Mixed Boundary Value Problems of the Theory of Elasticity in N-Dimensional Domains with Boundaries Containing Closed Cuspidal Edges”, Math. Nachr., 189 (1998), 61–105  crossref  mathscinet  zmath  isi
    4. Kokilashvili V. Meshveliani Z. Paatashvili V., “Boundary Value Problems for Analytic and Harmonic Functions of Smirnov Classes in Domains with Non-Smooth Boundaries”, Factorization, Singular Operators and Related Problems, Proceedings, ed. Samko S. Lebre A. DosSantos A., Springer, 2003, 175–196  mathscinet  isi
    5. Mazya V.G., Poborchii S.V., “O predstavlenii resheniya zadachi Neimana v oblasti s pikom garmonicheskim potentsialom prostogo sloya”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 3, 41–49  elib
    6. Mazya V.G., Poborchii S.V., “Odnoznachnaya razreshimost integralnogo uravneniya dlya garmonicheskogo potentsiala prostogo sloya na granitse oblasti s pikom”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 2, 63–73  elib
    7. Hyeonbae Kang, Hyundae Lee, KiHyun Yun, “Optimal estimates and asymptotics for the stress concentration between closely located stiff inclusions”, Math. Ann, 2015  crossref
    8. Bezrodnykh S. Bogatyrev A. Goreinov S. Grigor'ev O. Hakula H. Vuorinen M., “On Capacity Computation For Symmetric Polygonal Condensers”, J. Comput. Appl. Math., 361 (2019), 271–282  crossref  isi
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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