Boundary value problems for hypergenic function vectors

Abstract

Abstract This article mainly studies the boundary value problems for hypergenic function vectors in Clifford analysis. Firstly, some properties of hypergenic quasi-Cauchy type integrals are discussed. Then, by the Schauder fixed point theorem the existence of the solution to the nonlinear boundary value problem is proved. Finally, using the compression mapping principle the existence and uniqueness of the solution to the linear boundary value problem are proved.

Keywords

• Clifford analysis
• Hypergenic function vector
• Nonlinear boundary value problem
• Linear boundary value problem