On the Polynomial and Exponential Decay of Eigen-Vectors of Generalized Time-Harmonic Maxwell Problems

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 ⊂ RN , 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 in R \ {0} and that by means of Eidus’ limiting absorption principle a Fredholm alternative holds true.