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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 1, Pages 81–96
DOI: https://doi.org/10.26907/0021-3446-2021-1-81-96 (Mi ivm9642) 		 
Double- and simple-layer potentials for a three-dimensional elliptic equation with a singular coefficient and their applications

T. G. Ergashevab

a V.I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences, 81 Mirzo Ulugbek str., Tashkent, 100170 Republic of Uzbekistan
b Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazi str., Tashkent, 100000 Republic of Uzbekistan
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DOI: https://doi.org/10.26907/0021-3446-2021-1-81-96
Abstract: The double- and simple-layer potentials play an important role in solving boundary value problems for elliptic equations, and in studying this potentials, the properties of the fundamental solutions of the given equation are used. At present, fundamental solutions of the multidimensional Helmholtz equation are known but nevertheless, only for the two-dimensional equations the potential theory was constructed. In this paper we study both potentials for the three-dimensional singular elliptic equation and apply the obtained results to the solving a Dirichlet problem.
Keywords: double-layer potential, simple-layer potential, Green's function, fundamental solution, Dirichlet problem.
Received: 03.04.2020
Revised: 31.05.2020
Accepted: 29.06.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 1, Pages 72–86
DOI: https://doi.org/10.3103/S1066369X21010060
Bibliographic databases:
Document Type: Article
UDC: 517.946
Language: Russian
Citation: T. G. Ergashev, “Double- and simple-layer potentials for a three-dimensional elliptic equation with a singular coefficient and their applications”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 1, 81–96; Russian Math. (Iz. VUZ), 65:1 (2021), 72–86
Citation in format AMSBIB
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