Boundary Value Problems And Singular Integral Equations For Regular Functions In Clifford Analysis

In this dissertation, we establish the generalized Cauchy theorems and the generalized Cauchy integral formulae on the para-sphere in Clifford analysis. As their applications, the generalized Cauchy theorems and the generalized Cauchy integral formulae on the compact smooth surface and the cylindroid with crooked tips are respectively obtained. And these directly result in the Painleve theorem and the generalized Sochocki-Plemelj formula in Clifford analysis. Then, by using these results the jump Riemann boundary value problems and Dirichlet boundary value problems for regular functions in Clifford analysis are discussed. Some singular integral equations are also solved and the inver-sion formula for Cauchy principal value is obtained by these boundary value problems. Furthermore, Poincare-Bertrand formula on smooth surfaces are established.