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

2019/11/15 by Frank Osterbrink, Osterbrink, Frank, Dirk Pauly +1
Computer Science · Mathematics · #35Q60 #78A25 #78A30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1911.06871

openalex publication_date 2019/11/15 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We prove that the time-harmonic solutions to Maxwell's equations in a 3D\nexterior domain converge to a certain static solution as the frequency tends to\nzero. We work in weighted Sobolev spaces and construct new compactly supported\nreplacements for Dirichlet-Neumann fields. Moreover, we even show convergence\nin operator norm.\n

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