The generalized Holmgren problem for elliptic equation with several singular coefficients

2019/10/11 by Ergashev, Tuhtasin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.05264

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 generalized Holmgren 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.

Related

• The Dirichlet problem for elliptic equation with several singular coefficients
• Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain
• Some relations following from the decomposition formula for one\n multidimensional Lauricella hypergeometric function
• Fundamental solutions for a class of multidimensional elliptic equations\n with several singular coefficients
• Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables