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This paper treats the time-harmonic electro-magnetic scattering or radiationproblem governed by Maxwell's equations in an exterior weak Lipschitz domaindivided into two disjoint weak Lipschitz parts We will present a solutiontheory using the framework of polynomially weighted Sobolev spaces for therotation and divergence. We will show a Fredholm alternative type result tohold using the principle of limiting absorption introduced by Eidus in the1960's. The necessary a-priori-estimate and polynomial decay of eigenfunctionsfor the Maxwell equations will be obtained by transferring well known resultsfor the Helmholtz equation using a suitable decomposition of theelectro-magnetic fields. The crucial point for existence is a local version ofWeck's selection theorem, also called Maxwell compactness property.

Time-Harmonic Electro-Magnetic Scattering in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions