The Dirichlet problem for elliptic equation with several singular coefficients
Authors: Tuhtasin G. Ergashev
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2018 · Pages: 81 - 99
Published Online: 25 Jul 2019
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.
Keywords: Dirichlet problem, multidimensional elliptic equations, singular coefficients, decomposition formulas, Lauricella hypergeometric function