The Related Study Of Boundary Value Problems For Generalized Hypermonogenic Functions In Clifford Analysis

Clifford analysis studies the properties of functions defined on higher dimensional space and valued in Clifford algebra space of combination and noncommutativity.Its major research objects are monogenic functions and hypermonogenic functions,which is the generalization of analytic functions of one complex variable to the different manifolds in higher dimensional space.On the complex plane,analytic functions are the solution of the Laplace-Beltrami equations in Euclidean metric.The boundary value problem of Laplace-Beltrami equations is a hot issue in classical analysis,which studies the problem of the existence and uniqueness of the solution when equation meets a certain boundary conditions.Therefore it is an important issue to discuss the boundary value problems of the Laplace-Beltrami equations in various metrics by studying various functions and operators in Clifford analysis.This thesis focuses on the boundary value problems for generalized hypermonogenic functions and for generalized hypermonogenic vector valued functions.By decomposing the generalized hypermonogenic function into integral operators,it discusses the properties of some integral operators,the existence of the solution to the nonlinear boundary value problem for hypermonogenic functions.Based on this,it analyses the existence and uniqueness of the solution to the boundary value problems for generalized hypermonogenic vector valued function.This thesis consists of three chapters.Chapter 1 gives the related definitions and several important lemmas which is a necessity in our discussion.Chapter 2 firstly provides the integral representation of generalized hypermonogenic functions in Clifford analysis;secondly it discusses the Plemelj formula of generalized hypermonogenic functions;finally it explores the nonlinear boundary value problems.Chapter 3 firstly presents the definition of generalized hypermonogenic vector functions;secondly it examines the integral representation of generalized hypermonogenic vector functions;finally it addresses the linear boundary value problems for generalized hypermonogenic vector valued functions.