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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 12, Pages 2133–2154
DOI: https://doi.org/10.1134/S0044466919120044
(Mi zvmmf11006)
 

This article is cited in 1 scientific paper (total in 1 paper)

On the geometric properties of the Poisson kernel for the Lamé equation

A. O. Bagapshab

a Dorodnitsyn Computing Center, Russian Academy of Sciences, Moscow, 119991 Russia
b Bauman Moscow State Technical University, Moscow, 105005 Russia
Citations (1)
References:
Abstract: It is shown that the Poisson kernel for the Lamé equation in a disk can be interpreted as a bi-univalent mapping of the projection of an elliptic cone onto the projection of the surface of revolution of a hyperbola. The corresponding mapping $f_\sigma$ of these surfaces is bijective. Such an interpretation sheds light on the nature of the well-known special property of solutions of elliptic systems on a plane to map points to curves and vice versa. In particular, a singular point of the kernel under study can be considered as the projection of the cone element so that the mapping $f_\sigma$ is regular in the sense that this element is bijectively mapped into a curve.
Key words: elliptic systems, Lamé equation, non-univalent mappings.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00764
Ministry of Education and Science of the Russian Federation 1.3843.2017/4.6
This work was supported by the Russian Foundation for Basic Research (project no. 18-01-00764) and the Ministry of Education and Science of the Russian Federation (project no. 1.3843.2017/4.6).
Received: 25.07.2019
Revised: 25.07.2019
Accepted: 05.08.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 12, Pages 2124–2144
DOI: https://doi.org/10.1134/S0965542519120042
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. O. Bagapsh, “On the geometric properties of the Poisson kernel for the Lamé equation”, Zh. Vychisl. Mat. Mat. Fiz., 59:12 (2019), 2133–2154; Comput. Math. Math. Phys., 59:12 (2019), 2124–2144
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v59/i12/p2133
  • 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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    References:16
     
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