Riemann–Hilbert Problems for Biaxially Symmetric Monogenic Functions in \(\mathbb {R}^{n}\)

Abstract

We are dedicated to addressing Riemann–Hilbert boundary value problems (RHBVPs) with variable coefficients, where the solutions are valued in the Clifford algebra of \(\mathbb {R}_{0,n}\), for biaxially monogenic functions defined in the biaxially symmetric domains of the Euclidean space \(\mathbb {R}^{n}\). Our research establishes the equivalence between RHBVPs for biaxially monogenic functions defined in biaxially domains and RHBVPs for generalized analytic functions on the complex plane. We derive explicit solutions and conditions for solvability of RHBVPs for biaxially monogenic functions. Additionally, we explore related Schwarz problems and RHBVPs for biaxially meta-monogenic functions.