This article is cited in 10 papers

Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients

Tuhtasin G. Ergashev

Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Abstract: The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple hypergeometric functions and the decomposition formula is required for their investigation which would express the multivariable hypergeometric function in terms of products of several simpler hypergeometric functions involving fewer variables. In this paper, such a formula is proved instead of a previously existing recurrence formula.The order of singularity and other properties of the fundamental solutions that are necessary for solving boundary value problems for degenerate second-order elliptic equations are determined.

Keywords: multidimensional elliptic equation with several singular coefficients, fundamental solutions, decomposition formula.

UDC: 517.956.6; 517.44

Received: 13.09.2019
Received in revised form: 14.10.2019
Accepted: 04.12.2019

Language: English

DOI: 10.17516/1997-1397-2020-13-1-48-57

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