Boundary Value Problems For Some High-order Equations In Complex Plane And Clifford Analysis

Abstract:This paper mainly studies a class of Riemann boundary valueproblems for k-regular functions and equation kzWk = f in complex plane and theRiemann boundary value problem and its inverse problem for a class of generalizedk-regular functions in Cliord analysis.In chapter one,The formulation of a class of Riemann boundary value prob-lems for k-regular functions and equation kzWk = f are proposed.On the basisof the Riemann boundary value problems for k-Regular functions and equationkWzk = f, the solvability of Riemann boundary value problems of normal andnonnormal cases for k-regular functions and equation kzWk = f are discussed.Thetheorems of solvability of the problems are obtained.In chapter two,we discuss a class of Riemann boundary value problems and itsinverse problems for a class of generalized k-regular functions in Cliord analysis.Firstly we discuss some properties of generalized k-regular functions in Cliordanalysis,such as its Cauchy type integral, Plemelj's formula, and then consider theRiemann boundary value problem and its inverse problem,obtain the solvability of this problem and the integral representation of the solution to this problem.