Holmgren problem for Helmholtz equation with the three singular coefficients

Abstract

Fundamental solutions for a multidimensional Helmholtz equation with three singular coefficients have been constructed recently which are expressed in terms of the confluent hypergeometric function in four variables. In this paper, we study the Holmgren problem for a 3D elliptic equation with three singular coefficients. A unique solution of the problem is obtained in the explicit form.

Keywords

• holmgren problem
• multidimensional elliptic equations with three singular coefficients
• decomposition formulas
• lauricella hypergeometric function in three variables
• confluent hypergeometric function in four variables