Layer potential operators and a space of boundary data for electromagnetism in nonsmooth domains (Q1916877)

The layer potential singular integral operators arising in electromagnetic boundary value problems are studied in the context of domains bounded by Lipschitz or \(C^1\) boundaries. A boundary value problem for time harmonic electromagnetic waves corresponding to the scattering by a perfectly conducting surface is considered. The uniqueness of solution is shown in the case of arbitrary Lipschitz domains, while existence of solution and appropriate optimal estimates are obtained in the case of \(C^1\) domains. It is shown that the choice of space of boundary data plays a crucial role if the boundary values of the solutions are to be prescribed pointwise and not just in the distributional sense.