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Layer potential operators and a space of boundary data for electromagnetism in nonsmooth domains. (English) Zbl 0852.35138

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.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78A45 Diffraction, scattering
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