On a Riemann-Hilbert problem for9-hyperholomorphicfunctions in Rm

The purpose of this paper is to solve a kind of Riemann-Hilbert problem for Psi-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 Omega subset of 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+alpha, Gamma).

Automated summary

The purpose of this paper is to solve a Riemann-Hilbert problem for Psi-hyperholomorphic functions, which are connected with the use of non-standard orthogonal basis in Euclidean space R-m. The explicit solution of the problem in a Jordan domain Omega subset of R-m is obtained using Clifford analysis. The problem data involve Lipschitz class Lip(k-1+alpha, Gamma) due to the study's focus on smooth or fractal boundaries.