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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
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.
Received: 25.07.2019 Revised: 25.07.2019 Accepted: 05.08.2019
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11006 https://www.mathnet.ru/eng/zvmmf/v59/i12/p2133
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Abstract page: | 95 | References: | 16 |
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