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Sibirskii Zhurnal Industrial'noi Matematiki, 2012, Volume 15, Number 2, Pages 86–98 (Mi sjim728)  
This article is cited in 12 scientific papers (total in 12 papers)

On polynomial solutions to the Dirichlet problem for a biharmonic equation in a ball

V. V. Karachik, N. A. Antropova

South Ural State University, Chelyabinsk, Russia
Full-text PDF (250 kB) Citations (12)
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Abstract: We find a polynomial solution to the Dirichlet problem for an inhomogeneous biharmonic equation with polynomial right-hand side and polynomial boundary data in the unit ball. We use an explicit representation of harmonic functions in the Almansi formula.
Keywords: biharmonic equation, harmonic polynomials, Dirichlet problem, polynomial solutions, Almansi formula.
Received: 08.07.2011
Bibliographic databases:
Document Type: Article
UDC: 517.956.225+517.575
Language: Russian
Citation: V. V. Karachik, N. A. Antropova, “On polynomial solutions to the Dirichlet problem for a biharmonic equation in a ball”, Sib. Zh. Ind. Mat., 15:2 (2012), 86–98
Citation in format AMSBIB
\Bibitem{KarAnt12}
\by V.~V.~Karachik, N.~A.~Antropova
\paper On polynomial solutions to the Dirichlet problem for a~biharmonic equation in a~ball
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 2
\pages 86--98
\mathnet{http://mi.mathnet.ru/sjim728}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3099837}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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