Fundamental solutions of a multidimensional degenerate elliptic equation

Fundamental solutions of a two-dimensional degenerate elliptic equation have recently become known which are expressed via the Appell hypergeometric function. The main result of the present paper is the construction of fundamental solutions for a class of multidimensional degenerate elliptic equations. These fundamental solutions are directly connected with multiple hypergeometric function of Lauricella and their properties. In this paper, new properties of the Lauricella hypergeometric function are established, which allow finding fundamental solutions of the considered equation in explicit forms. In addition, the properties of the constructed fundamental solutions, which are necessary in the future for solving boundary value problems for a multidimensional degenerate elliptic equation, are investigated.

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