English

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

Analysis of PDEs 2011-05-23 v1 Mathematical Physics Differential Geometry math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1105.4105,
  title  = {On the Polynomial and Exponential Decay of Eigen-Forms of Generalized Time-Harmonic Maxwell Problems},
  author = {Dirk Pauly},
  journal= {arXiv preprint arXiv:1105.4105},
  year   = {2011}
}

Comments

Key Words: Maxwell's equations, exterior boundary value problems, radiating solutions, polynomial and exponential decay of eigensolutions, variable coefficients, electro-magnetic theory