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Fundamentalnaya i Prikladnaya Matematika, 2002, Volume 8, Issue 4, Pages 1129–1158 (Mi fpm702)  

This article is cited in 1 scientific paper (total in 1 paper)

On the mixed problem for Laplace equation outside cuts, placed along a circumference in a plane

A. I. Sgibnev, P. A. Krutitskii

M. V. Lomonosov Moscow State University
Full-text PDF (937 kB) Citations (1)
References:
Abstract: The boundary value problem for harmonic functions outside cuts lying on the arcs of a circumference is considered. The Dirichlet condition is given on one side of each cut and Neumann condition is specified on the other side. The problem is reduced to the Riemann–Hilbert problem for complex analytic function, which is solved in a closed form. An explicit solution of the original problem is obtained.
Received: 01.01.2001
Bibliographic databases:
UDC: 517.956.225
Language: Russian
Citation: A. I. Sgibnev, P. A. Krutitskii, “On the mixed problem for Laplace equation outside cuts, placed along a circumference in a plane”, Fundam. Prikl. Mat., 8:4 (2002), 1129–1158
Citation in format AMSBIB
\Bibitem{SgiKru02}
\by A.~I.~Sgibnev, P.~A.~Krutitskii
\paper On the mixed problem for Laplace equation outside cuts, placed along a~circumference in a~plane
\jour Fundam. Prikl. Mat.
\yr 2002
\vol 8
\issue 4
\pages 1129--1158
\mathnet{http://mi.mathnet.ru/fpm702}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1972583}
\zmath{https://zbmath.org/?q=an:1050.35064}
Linking options:
  • https://www.mathnet.ru/eng/fpm702
  • https://www.mathnet.ru/eng/fpm/v8/i4/p1129
  • This publication is cited in the following 1 articles:
    1. Krutitskii P.A., Sgibnev A.I., “Singularities of the solution gradient in the generalized jump problem for the Laplace equation outside a cut on the plane”, Differ. Equ., 39:9 (2003), 1225–1236  mathnet  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
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    Abstract page:503
    Full-text PDF :158
    References:79
    First page:1
     
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