# The Dirichlet problem for elliptic equation with several singular coefficients

## TL;DR

This paper derives explicit solutions for the Dirichlet problem of a multidimensional singular elliptic equation using Lauricella hypergeometric functions, advancing understanding of such equations with multiple singular coefficients.

## Contribution

It provides a unique explicit solution to the Dirichlet problem for elliptic equations with multiple singular coefficients, utilizing Lauricella hypergeometric functions and their properties.

## Key findings

- Explicit solutions expressed via Lauricella hypergeometric functions
- Use of decomposition formulas and adjacent relations for solution derivation
- Advancement in solving multidimensional singular elliptic equations

## 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.