We study time-dependent and time-harmonic Maxwell's equations in a bounded, simply connected Lipschitz domain Ω. Absorbing boundary conditions are used so that uniformly traveling electromagnetic waves arriving at the boundary in a given direction can be completely transmitted. A generalized Green's theorem on is used in treating initial boundary value and boundary value problems. Energy estimates for the time-dependent problem are given. For the time-harmonic problem, given L²-electric and magnetic current densities, electromagnetic field intensities are shown to exist uniquely in the space . An integral representation is also given.
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Dongwoo Sheen (1997) studied this question.
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