Boundary Value Problem For Some Partial Differential Equations In Quaternion Analysis

This paper mainly discusses boundary value problems for some partial differential equations in quaternion analysis by theory of complex analysis. The paper is divided into two chapters.In chapter one,The Riemann boundary value problem with conjugate value for n-regular vector function is discussed. Firstly this problem is translated into a singular integral equation by n-regular vector function with Plemelj formula. Then the existence and uniqueness of the solution for this problem are proved by using the theory of singular equation and the contract mapping theorem.In chapter two,The Riemann boundary value problem with conjugate value for n-regular function in quaternion space is considered by methods used in chapter one. Firstly this problem is translated into a singular integral equation by n-regular function with Plemelj formula. Then the existence and uniqueness of the solution for this problem are proved by using the theory of singular equation and the contract mapping theorem.