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

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

2011-05-20

arxiv.org/abs/1105.4105v1

Mathematics

Analysis of PDEs

Key Words: Maxwell's equations, exterior boundary value problems, radiating solutions, polynomial and exponential decay of eig

Scientific paper

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 with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate 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.

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