On Boundary Problems for Regular Functions in Hypercomplex Analysis

Abstract

In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized Cauchy theorem, the generalized Cauchy integral formula, the Painlev\'{e} theorem and boundary behaviors of the Cauchy type integrals, as well as various integral representations. Certain boundary value problems in the Clifford algebra setting and singular integral equations are introduced.