Generalized Maxwell Equations in Exterior Domains II: Radiation Problems and Low Frequency Behavior

We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in an exterior domain Ω ⊂ RN , N ≥ 3 , with nonsmooth inhomogeneous, anisotropic coefficients converging near infinity with a rate r−τ , τ > 1 , towards the identity. By means of the limiting absorption principle we prove for real frequencies that a Fredholm alternative holds true, that eigensolutions decay polynomially resp. exponentially at infinity and that the corresponding eigenvalues do not accumulate even at zero. Then we show the convergence of the time-harmonic solutions to a solution of an electro-magneto static Maxwell system as the frequency tends to zero. Finally we are able to generalize these results to the corresponding Maxwell system with inhomogeneous boundary data.