Generalized Holmgren Problem for an Elliptic Equation withSeveral Singular Coefficients

It has recently been established that all fundamental solutions of a multidimensional singular elliptic equation can be expressed via the well-known multivariate Lauricella hypergeometric function. In the present paper, we prove that the generalized Holmgren problem for an elliptic equation with several singular coefficients has a unique solution and find this solution in closed form. When finding the solution, we use decomposition formulas and some contiguous relationships for the multivariate Lauricella hypergeometric function.