Dirichlet Boundary Value Problem For Some Partial Differential Equations In Quaternionic Analysis

In this paper,we mainly discuss Dirichlet problems of some elliptic equa-tion and in quaternion space and obtain the integral representation of general solutions.In chapter one,we discuss the Dirichlet boundary value problems of the first vector field on electromagnetic field in quasi-quaternion space,and obtain the integral representation of general solutions.In chapter two,we discuss the Dirichlet boundary value problems of the second vector field on electromagnetic field in quasi-quaternion space,and obtain the integral represen-tation of general solutions.In chapter three,we discuss the Dirichlet boundary value problems of the third vector field on electromagnetic field in quasi-quaternion space,and obtain the integral represen-tation of general solutions.In chapter four,we discuss the Dirichlet boundary value problems of the fourth vector field on electromagnetic field in quasi-quaternion space,and obtain the integral represen-tation of general solutions.In chapter five,on the basis of the text [10],by creating methods from complex analysis and quaternionic analysis, we discuss the Dirichlet boundary value problems of regular vector function and the equation of n-order such as (?)F=u.