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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 8, Pages 1295–1308
DOI: https://doi.org/10.31857/S0044466921040050 (Mi zvmmf11277) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation

V. V. Karachik

South Ural State University, 454080, Chelyabinsk, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466921040050
Abstract: The solvability of one class of Neumann-type problems for the homogeneous polyharmonic equation in the unit ball is investigated. First, local sufficient conditions for the solvability of Neumann-type problems are obtained; then they are transformed to boundary conditions in integral form as conditions of orthogonality on the unit sphere of homogeneous harmonic polynomials of some degrees to linear combinations of boundary functions with coefficients from the integer Neumann triangle. These sufficient conditions are identical to the previously obtained set of necessary conditions for the solvability of the Neumann-type problems under consideration. An example is considered.
Key words: polyharmonic equation, necessary and sufficient conditions, solvability, Neumann-type problems.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.А03.21.0011
This work was supported by the Government of the Russian Federation (Resolution no. 211 of March 16, 2013), agreement no. 02.A03.21.0011.
Received: 24.06.2020
Revised: 12.11.2020
Accepted: 16.12.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 8, Pages 1276–1288
DOI: https://doi.org/10.1134/S0965542521040059
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: Russian
Citation: V. V. Karachik, “Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation”, Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021), 1295–1308; Comput. Math. Math. Phys., 61:8 (2021), 1276–1288
Citation in format AMSBIB
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\paper Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation
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\vol 61
\issue 8
\pages 1295--1308
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\transl
\jour Comput. Math. Math. Phys.
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\pages 1276--1288
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  • https://www.mathnet.ru/eng/zvmmf/v61/i8/p1295
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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