On a Riemann-Hilbert boundary value problem for $(\phi ,\psi )$-harmonic functions in ${\mathbb{R}}^m$

Abstract

The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for $(\phi ,\psi )$-harmonic functions, which are linked with the use of two orthogonal basis of the Euclidean space ${\mathbb{R}}^m$. We approach this problem using the language of Clifford analysis for obtaining the explicit expression of the solution of the problem in a Jordan domain $\Omega \subset {\mathbb{R}}^m$ with fractal boundary. One of the remarkable feature in this study is that the boundary data involves higher order Lipschitz class of functions.

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