Some Boundary Value Problems For HyperMonogenic Functions And Generalized Regular Functions In Clifford Analysis

The complex analysis method is a powerful tool for studying partial differential equations.In this paper,we mainly study some boundary value problems of hypermonogenic functions and generalized regular functions in Clifford analysis , the oblique derivative boundary value problem for a degenerate hyperbolic eqution of second order in plane,we generalize some results in recent literature.Firstly,in Clifford analysis ,we study the Plemelj formula of generalized regular functions, obtain the integral representations of solutions about generalized regular functions for a class of Riemann boundary value problem ,and prove the linear boundary value problem has a unique solution,Moreover,the mathematical formulation of a class of inverse Riemann boundary value problem for generalized regular functions is presented,then we transfer this inverse problem into Riemann boundary value problem.Secondly,we study some properties about hypermonogenic functions in Clifford analysis (the solution of the equation M_n-1¹ f(x) =0,where M_k^k f( x)=D₁ f(x)+ k(Q'f/x_n)f∈F_D^r(r >1), k = 0, 1,,n-1),applying the method of singular integral equation and the Schauder fixed point theorem,...