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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 12, Pages 2065–2072
DOI: https://doi.org/10.7868/S0044466916120048 (Mi zvmmf10495) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The Poisson integral and Green's function for one strongly elliptic system of equations in a circle and an ellipse

A. O. Bagapshab

a Bauman Moscow State Technical University, Moscow, Russia
b Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia
Full-text PDF (171 kB) Citations (4)
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DOI: https://doi.org/10.7868/S0044466916120048
Abstract: For a strongly elliptic system of second-order equations of a special form, formulas for the Poisson integral and Green's function in a circle and an ellipse are obtained. The operator under consideration is represented by the sum of the Laplacian and a residual part with a small parameter, and the solution to the Dirichlet problem is found in the form of a series in powers of this parameter. The Poisson formula is obtained by the summation of this series.
Key words: elliptic systems, Dirichlet problem, Poisson integral, Green's function.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.2640.2014
НШ-9110.2016.1
Russian Foundation for Basic Research 16-01- 00674_а
Received: 20.05.2016
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 12, Pages 2035–2042
DOI: https://doi.org/10.1134/S0965542516120046
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: A. O. Bagapsh, “The Poisson integral and Green's function for one strongly elliptic system of equations in a circle and an ellipse”, Zh. Vychisl. Mat. Mat. Fiz., 56:12 (2016), 2065–2072; Comput. Math. Math. Phys., 56:12 (2016), 2035–2042
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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