Clifford分析中无界域上正则函数的边值问题

The Boundary Value Problem for Regular Functions on Unbounded Domains in Clifford Analysis

在引入修正Cauchy核的基础上,讨论了无界域上正则函数的带共轭值的边值问题：a(t)Φ+(t)+b(t)Φ+(t)+c(t)Φ-(t)+d(t)Φ=g(t)．首先给出了无界域上正则函数的Plemelj公式,然后利用积分方程方法和压缩不动点原理证明了问题解的存在唯一性．

On the basis of the introduction of the modified Cauchy kernel, this paper deals with the boundary value problem with conjugate value for regular functions on unbounded domains：α（t）φ^＋（t）＋b（t）φ^＋（t）＋c（t）φ^-（t）＋d（t）φ^＋（t）=g（t）Firstly, we give the Plemely formula for regular functions on unbounded domains. Then, bv the integral equation method and the fixed point theorem, we prove the existence and uniqueness of the solution for the problem.