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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2020, Volume 5, Issue 4(1), Pages 391–399
DOI: https://doi.org/10.47475/2500-0101-2020-15401 (Mi chfmj196) 		 
Mathematics

Presentation of solution of the Dirichlet problem for biharmonic equation in the unit ball through the Green function

V. V. Karachik

South Ural State University (National Research University), Chelyabinsk, Russia
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DOI: https://doi.org/10.47475/2500-0101-2020-15401
Abstract: A representation of the solution of the Dirichlet problem for the biharmonic equation in the unit ball through the Green function of the problem is obtained. Using the Green function, which was found earlier, first, the case of simple polynomial boundary conditions is investigated. Then the formula, which is obtained in the simple case, is proved for the boundary data of the general Dirichlet problem.
Keywords: Green function, biharmonic equation, Dirichlet problem.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
The work was supported by Act 211 of Government of the Russian Federation, contract 02.A03.21.0011.
Received: 06.07.2020
Revised: 21.09.2020
Document Type: Article
UDC: 519.635.1+517.956.223
Language: Russian
Citation: V. V. Karachik, “Presentation of solution of the Dirichlet problem for biharmonic equation in the unit ball through the Green function”, Chelyab. Fiz.-Mat. Zh., 5:4(1) (2020), 391–399
Citation in format AMSBIB
\Bibitem{Kar20}
\by V.~V.~Karachik
\paper Presentation of solution of the Dirichlet problem
for biharmonic equation in the unit ball through the Green function
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2020
\vol 5
\issue 4(1)
\pages 391--399
\mathnet{http://mi.mathnet.ru/chfmj196}
\crossref{https://doi.org/10.47475/2500-0101-2020-15401}
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