混合边界条件下外弱 Lipschitz 域中时谐 Maxwell 方程的低频渐近性与电磁静力学
偏微分方程分析
2020-07-20 v3 数学物理
泛函分析
math.MP
摘要
我们证明了当频率趋于零时，三维外域中 Maxwell 方程的时谐解收敛到某个静态解。我们在加权 Sobolev 空间中工作，并构造了 Dirichlet-Neumann 场的新的紧支撑替代。此外，我们甚至证明了在算子范数下的收敛性。
引用
@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}
}
备注
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