Time-Harmonic Electro-Magnetic Scattering in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions
Abstract
This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using the framework of polynomially weighted Sobolev spaces for the rotation and divergence. We will show a Fredholm alternative type result to hold using the principle of limiting absorption introduced by Eidus in the 1960's. The necessary a-priori-estimate and polynomial decay of eigenfunctions for the Maxwell equations will be obtained by transferring well known results for the Helmholtz equation using a suitable decomposition of the electro-magnetic fields. The crucial point for existence is a local version of Weck's selection theorem, also called Maxwell compactness property.
Keywords
Cite
@article{arxiv.1809.01117,
title = {Time-Harmonic Electro-Magnetic Scattering in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions},
author = {Frank Osterbrink and Dirk Pauly},
journal= {arXiv preprint arXiv:1809.01117},
year = {2019}
}
Comments
key words: Maxwell equations, radiating solutions, exterior boundary value problems, polynomial decay, mixed boundary conditions, weighted Sobolev spaces, Hodge{\DH}Helmholtz decompositions