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arXiv · 2005.07868

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

José Luis Serrano Ricardo·Ricardo Abreu Blaya·Juan Bory Reyes·Jorge Sánchez Ortiz
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Abstract

The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for $(\varphi,\psi)$-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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José Luis Serrano Ricardo, Ricardo Abreu Blaya, Juan Bory Reyes, Jorge Sánchez Ortiz. 2020-05-16. On a Riemann-Hilbert boundary value problem for $(\varphi,\psi)$-harmonic functions in $\mathbb{R}^m$. https://arxiv.org/abs/2005.07868

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