  This paper treats the time-harmonic electro-magnetic scattering or radiation
problem governed by Maxwell's equations in an exterior weak Lipschitz domain
divided into two disjoint weak Lipschitz parts We will present a solution
theory using the framework of polynomially weighted Sobolev spaces for the
rotation and divergence. We will show a Fredholm alternative type result to
hold using the principle of limiting absorption introduced by Eidus in the
1960's. The necessary a-priori-estimate and polynomial decay of eigenfunctions
for the Maxwell equations will be obtained by transferring well known results
for the Helmholtz equation using a suitable decomposition of the
electro-magnetic fields. The crucial point for existence is a local version of
Weck's selection theorem, also called Maxwell compactness property.
