Reconstruction of solutions to a generalized Moisil-Teodorescu system in Jordan domains with rectfiable boundary

TL;DR

This paper addresses the reconstruction of solutions to a generalized Moisil-Teodorescu system within Jordan domains in three-dimensional space, utilizing quaternionic embedding to establish existence conditions.

Contribution

It introduces a quaternionic framework to analyze the generalized Moisil-Teodorescu system and derives conditions for the existence of solutions in domains with rectifiable boundaries.

Findings

Established existence conditions for solutions

Embedded the system in a quaternionic setting

Analyzed solutions in Jordan domains

Abstract

In this paper we consider the problem of reconstructing solutions to a generalized Moisil-Teodorescu system in Jordan domains of $\mathbb{R}^{3}$ with rectifiable boundary. In order to determine conditions for existence of solutions to the problem we embed the system in an appropriate generalized quaternionic setting.