Clifford分析中广义超正则函数向量的非线性边值问题

Nonlinear Boundary Value Problem for Generalized Hypermonogenic Function Vector in Clifford Analysis

利用Cauchy型奇异积分算子的性质讨论Clifford分析中一类广义超正则函数向量的积分表达式,并利用Schauder不动点原理证明这类广义超正则函数向量非线性边值问题的可解性,最后给出解的表达式.

We discussed the integral expression of a kind of generalized hypermonogenic function vector in Clifford analysis by using the properties of some Cauchy-type singular integral operators. Then we proved the solvability of the nonlinear boundary value problem for the kind of generalized hypermonogenic function vector by using the Schauder fixed point theorem, and gave the expression of the solution.