On a Riemann - Hilbert boundary value problem for (φ,ψ)-harmonic functions in ℝ^m

The purpose of this paper is to solve a kind of the Riemann-Hilbert boundary value problem for (φ, ψ) -harmonic functions, which are linked with the use of two orthogonal bases of the Euclidean space ℝm. We approach this problem using the language of Clifford analysis for obtaining an explicit expression of the solution of the problem in a Jordan domain Ω ⊂ ℝm with fractal boundary. Since our study is concerned with a second order differential operator, the boundary data are restricted to involve the higher order Lipschitz class Lip (1 + α, Γ).