2D Quaternionic Time-Harmonic Maxwell System in Elliptic Coordinates

In this paper we consider the 2D time–harmonic Maxwell equations in elliptic coordinates through certain quaternionic perturbed Dirac operator. The main goal is aimed to analyze an electromagnetic Dirichlet problem for a curvilinear polygon with rectifiable boundary in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^2}$$\end{document}. In addition, we provide an integral representation formula for electromagnetic fields that resembles the classical Stratton-Chu formula. The importance of the problem for applications makes it worthy of consideration.