Low Frequency Asymptotics and Electro-Magneto-Statics for Time-Harmonic Maxwell's Equations in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions

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 sh...

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Bibliographic Details
Published in:arXiv.org 2020-07
Main Authors: Osterbrink, Frank, Pauly, Dirk
Format: Article
Language:English
Subjects:
Boundary conditions
Convergence
Dirichlet problem
Domains
Mathematical analysis
Maxwell's equations
Sobolev space
Online Access:Get full text
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Summary: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.
ISSN:2331-8422