Solutions of inhomogeneous perturbed generalized Moisil-Teodorescu system and Maxwell's equations in Euclidean Space

TL;DR

This paper establishes solvability conditions for inhomogeneous perturbed generalized Moisil-Teodorescu systems and Maxwell's equations in higher-dimensional Euclidean spaces using complex Clifford analysis.

Contribution

It introduces a new approach based on generalized conjugate harmonic pairs to determine solvability conditions for these systems.

Findings

Derived necessary and sufficient solvability conditions

Extended results to Maxwell's equations in higher dimensions

Utilized complex Clifford analysis framework

Abstract

In this paper, based on a proposed notion of generalized conjugate harmonic pairs in the framework of complex Clifford analysis, necessary and sufficient conditions for the solvability of inhomogeneous perturbed generalized Moisil-Teodorescu systems in higher dimensional Euclidean spaces are proved. As an application, we derive corresponding solvability conditions for the inhomogeneous Maxwell's equations.