A kind of Riemann and Hilbert boundary value problem for left monogenic functions in Rm (m ≥ 2)

Abstract

In this article, some properties of Cauchy-type integral and singular integral with integration domain are discussed, especially their boundary value properties at ∞. With the help of Painlevé theorem and Liouville theorem, a Riemann Boundary Value Problem (BVP for short) and a Hilbert BVP for left monogenic functions in Clifford analysis are investigated in the classical sense, their explicit representation of solutions are obtained respectively.