On polynomial and exponential decay of eigen-solutions to exterior boundary value problems for the generalized time-harmonic Maxwell system

We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain Ω⊂R^N, N≥1, with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a rate r^−τ, τ>1, towards the identity. As a canonical application we show that the corresponding eigen-values do not accumulate and that by means of Eidus' limiting absorption principle a Fredholm alternative holds true.