Clifford分析中广义超正则函数的一个非线性边值问题

A Nonlinear Boundary Value Problem for the Generalized Hypermonogenic Functions In Clifford Analysis

讨论了Cliffrd分析中广义超正则函数的一个非线性边值问题.首先将广义超正则函数分解为两个奇异积分算子,然后给出了广义超正则函数的Plemelj公式及相关奇异积分算子的性质,最后利用Schauder不动点原理证明了广义超正则函数的一个非线性边值问题的解的存在性及积分表达式.

This paper discusses a nonlinear boundary value problem for generalized hyper- monogenic functions in Clifford analysis. First we decompose the generalized hypermono- genic functions into the sum of two singular integral operators. Then we give the Plemelj formula for generalized hypermonogenic functions and discuss the properties of these integral operators. At last we prove the existence of the solution to the nonlinear boundary value problem for the generalized hypermonogenic functions in Clifford analysis by the Schauder fixed point theorem and give the integral expression of the solution.