2D quaternionic time-harmonic Maxwell system in elliptic coordinates. (English) Zbl 1319.35253
Summary: 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 \(\mathbb{R}^2\). 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.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35Q40 | PDEs in connection with quantum mechanics |
| 78A25 | Electromagnetic theory (general) |
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