The Dirichlet problem for elliptic equation with several singular coefficients

Abstract

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. When finding a solution, we use decomposition formulas and some adjacent relations for the Lauricella hypergeometric function in many variables.

Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables

“…However, due to the recurrence of the formula (3.4), additional difficulties may arise in the applications of this expansion. Further study of the properties of operators (3.2) and (3.3) showed that formula (3.4) can be reduced to a more convenient form [21]…”