Low Frequency Asymptotics and Electro-Magneto-Statics for Time-Harmonic Maxwell's Equations in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions
Analysis of PDEs
2020-07-20 v3 Mathematical Physics
Functional Analysis
math.MP
Abstract
We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported replacements for Dirichlet-Neumann fields. Moreover, we even show convergence in operator norm.
Keywords
Cite
@article{arxiv.1911.06871,
title = {Low Frequency Asymptotics and Electro-Magneto-Statics for Time-Harmonic Maxwell's Equations in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions},
author = {Frank Osterbrink and Dirk Pauly},
journal= {arXiv preprint arXiv:1911.06871},
year = {2020}
}
Comments
keywords: low frequency asymptotics, exterior boundary value problems, Maxwell's equations, electro-magneto-statics, Hodge-Helmholtz decompositions, radiating solutions, Dirichlet-Neumann fields, cohomology groups, polynomial decay of eigensolutions