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

2020/05/16 by José Luis Serrano Ricardo, Ricardo, José Luis Serrano, Ricardo Abreu Blaya +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2005.07868

openalex publication_date 2020/05/16 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for (φ,ψ)-harmonic functions, which are linked with the use of two orthogonal basis of the Euclidean space 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 Ω⊂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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