This article is cited in 6 papers

A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain

T. G. Ergashev^a, Z. R. Tulakova<sup>b

a</sup> «Tashkent Institute of Irrigation and Agricultural Mechanization Engineers» National Research University, 39 Kari Niyazi str., Tashkent, 100000 Republic of Uzbekistan
^b Fergana Branch of the Tashkent University of Information Technologies, 185 Mustakillik str., Fergana, 100118 Republic of Uzbekistan

Abstract: Solutions of the Dirichlet and Neumann problems for multidimensional singular elliptic equations in an infinite domain were found in explicit forms in recent works of the authors. In this paper, a problem with mixed conditions, which is a natural generalization of the previously considered Dirichlet and Neumann problems, is studied. In proving the existence of a unique solution to the problem posed, representation of the multiple Lauricella hypergeometric function at limiting values of the variables and a new formula for multiple improper integrals, which generalizes the well-known formula from the handbook of I.S. Gradshtein and I.M. Ryzhik, are used.

Keywords: Problem with mixed boundary conditions in an infinite domain, multidimensional elliptic equation with singular coefficients, fundamental solution, formula for the limit values of a hypergeometric function, Lauricella hypergeometric function of several variables.

UDC: 517.946

Received: 28.09.2021
Revised: 11.11.2021
Accepted: 23.12.2021

DOI: 10.26907/0021-3446-2022-7-58-72

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2022, 66:7, 51–63