Abstract:
At present, the fundamental solutions of the multidimensional singular elliptic equation are known and they are expressed in terms of the well-known Lauricella hypergeometric function of several variables. In this paper, we study the Dirichlet problem for an elliptic equation with several singular coefficients in an unbounded domain. When finding the solution to the posed problem, the expansion and summation formulas , as well as the limit relation for the Lauricella hypergeometric function of several variables are used.
Keywords:
Dirichlet problem, multidimensional elliptic equations with several singular coefficients, decomposition formulas, Lauricella hypergeometric function of many variables.
Citation:
T. G. Ergashev, Z. R. Tulakova, “The Dirichlet problem for an elliptic equation with several singular coefficients in an infinite domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 7, 81–91; Russian Math. (Iz. VUZ), 65:7 (2021), 71–80
\Bibitem{ErgTul21}
\by T.~G.~Ergashev, Z.~R.~Tulakova
\paper The Dirichlet problem for an elliptic equation with several singular coefficients in an infinite domain
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 7
\pages 81--91
\mathnet{http://mi.mathnet.ru/ivm9697}
\crossref{https://doi.org/10.26907/0021-3446-2021-7-81-91}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 7
\pages 71--80
\crossref{https://doi.org/10.3103/S1066369X21070082}
Linking options:
https://www.mathnet.ru/eng/ivm9697
https://www.mathnet.ru/eng/ivm/y2021/i7/p81
This publication is cited in the following 4 articles:
Otadavlat Nasriddinov, Jamoliddin Abdullayev, Dilnavoz Jo'rayeva, Nasiba Botirova, Oybek Maniyozov, Odilakhon Isomiddinova, V. Tsypko, S. Yekimov, A. Bieliatynskyi, “In biology, solving a problem coming to a differential equation in the maple program”, E3S Web of Conf., 508 (2024), 04006
T. G. Ergashev, A. Hasanov, T. K. Yuldashev, “Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation”, Lobachevskii J Math, 45:3 (2024), 1072
T. G. Ergashev, Z. R. Tulakova, “A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain”, Russian Math. (Iz. VUZ), 66:7 (2022), 51–63
T. G. Ergashev, Z. R. Tulakova, “The Neumann Problem for a Multidimensional Elliptic Equation with Several Singular Coefficients in an Infinite Domain”, Lobachevskii J Math, 43:1 (2022), 199