标题： Lauricella超几何函数及其在无限域中具有多个奇异系数的多维椭圆方程的Neumann问题解中的应用 显示英文标题

标题： 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

摘要： 目前，具有多个奇异系数的多维椭圆方程的基本解是已知的，并且它们用多变量Lauricella超几何函数来表示。 在本文中，我们研究了无限域中具有多个奇异系数的多维椭圆方程的Neumann问题。 利用积分能量的方法，证明了解的唯一性。 在证明Neumann问题显式解的存在性过程中，使用了一个微分公式、Lauricella超几何函数的一些相邻和极限关系以及一些多维非正常积分的值。 显示英文摘要

摘要： At present, the fundamental solutions of the multidimensional elliptic equation with the several singular coefficients are known and they are expressed in terms of the Lauricella hypergeometric function of many variables. In this paper we study the Neumann problem for a multidimensional elliptic equation with several singular coefficients in the infinite domain. Using the method of the integral energy the uniqueness of solution has been proved. In the course of proving the existence of the explicit solution of the Neumann problem, a differentiation formula, some adjacent and limiting relations for the Lauricella hypergeometric functions and the values of some multidimensional improper integrals are used.