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Fundamentalnaya i Prikladnaya Matematika, 2006, Volume 12, Issue 6, Pages 115–135 (Mi fpm993)  
This article is cited in 2 scientific papers (total in 2 papers)

The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a plane

P. A. Krutitskiia, A. I. Sgibnevb

a M. V. Lomonosov Moscow State University, Faculty of Physics
b M. V. Lomonosov Moscow State University
Full-text PDF (207 kB) Citations (2)
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Abstract: We consider the mixed problem for Laplace's equation outside cuts in a plane. The Dirichlet boundary condition is posed on one side of each cut, and the skew derivative condition is posed on the other side. This problem generalizes the mixed Dirichlet–Neumann problem. Using the method of potentials, this problem is reduced to a uniquely solvable Fredholm integral equation of the second kind.
English version:
Journal of Mathematical Sciences (New York), 2008, Volume 151, Issue 1, Pages 2710–2725
DOI: https://doi.org/10.1007/s10948-008-0168-8
Bibliographic databases:
UDC: 517.958+517.968
Language: Russian
Citation: P. A. Krutitskii, A. I. Sgibnev, “The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a plane”, Fundam. Prikl. Mat., 12:6 (2006), 115–135; J. Math. Sci., 151:1 (2008), 2710–2725
Citation in format AMSBIB
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\by P.~A.~Krutitskii, A.~I.~Sgibnev
\paper The method of integral equations for the mixed problem with the skew derivative for harmonic functions outside cuts in a~plane
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 6
\pages 115--135
\mathnet{http://mi.mathnet.ru/fpm993}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2314135}
\zmath{https://zbmath.org/?q=an:1151.35327}
\elib{https://elibrary.ru/item.asp?id=11143811}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 151
\issue 1
\pages 2710--2725
\crossref{https://doi.org/10.1007/s10948-008-0168-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42449145213}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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