Contents I. Introduction
Let be a smooth, simply connected domain in with boundary and unit outward normal . Let and denote the electric and magnetic field intensities respectively, where the time variable belongs to some interval . Given a current density function , specifying the applied current, Maxwell's equations state that \begin{align*} \varepsilon \mathbf{E}_{t}+\sigma \mathbf{E}-\nabla\times \mathbf{H}=\mathbf{J}\quad \text{in}\ \Omega\times(0, T),\tag{1}\\ \mu \mathbf{H}_{t}+\nabla\times \mathbf{E}=0\quad \text{in}\ \Omega\times(0, T). \tag{2} \end{align*}
