Lauricella超几何函数及其在无穷域上多奇异系数多维椭圆型方程Neumann问题解中的应用
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：
目前已知多维多奇异系数椭圆型方程的基本解是用多元Lauricella超几何函数表示的。本文研究了无穷区域上具有多个奇异系数的多维椭圆型方程的Neumann问题。利用积分能量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，利用了一个微分公式、Lauricella超几何函数的一些相邻关系和极限关系以及一些多维反常积分的值.
英文摘要：
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.
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