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

Author

Ricardo, José Luis Serrano, Blaya, Ricardo Abreu, Reyes, Juan Bory, and Ortiz, Jorge Sánchez

Subjects
Mathematics - Analysis of PDEs
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., Comment: 9 pages 0 figures

Published
2020

4. On a Riemann–Hilbert problem for Ψ-hyperholomorphic functions in Rm.

Author

Ricardo, José Luis Serrano, Blaya, Ricardo Abreu, and Ortiz, Jorge Sánchez

Abstract

The purpose of this paper is to solve a kind of Riemann–Hilbert problem for Ψ -hyperholomorphic functions, which are linked with the use of non-standard orthogonal basis of the Euclidean space R m . We approach this problem using the language of Clifford analysis for obtaining the explicit solution of the problem in a Jordan domain Ω ⊂ R m . Since our study is concerned with either a smooth or fractal boundary, the data of the problem involve Lipschitz class Lip (k - 1 + α , Γ) . [ABSTRACT FROM AUTHOR]

Published
2023
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