Quantitative trace estimates for the Maxwell system in Lipschitz domains

We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the Lipschitz character of the domain. We pay special attention to trace operators and extension operators over certain Sobolev spaces. Finally, we...

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Bibliographic Details
Published in:	Mathematical methods in the applied sciences 2021-09, Vol.44 (13), p.10635-10652
Main Authors:	Stachura, Eric, Wellander, Niklas
Format:	Article
Language:	eng
Subjects:	Domains electromagnetic scattering Estimates Lipschitz domains Maxwell equations Operators scattered fields Sobolev space trace theorems
Online Access:	Request full text
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Summary:	We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the Lipschitz character of the domain. We pay special attention to trace operators and extension operators over certain Sobolev spaces. Finally, we provide a weak formulation of the interior scattering problem in terms of the exterior Calderón operator and provide explicit bounds for the solution of the interior problem in terms of the incident fields and the Lipschitz character of the domain.
ISSN:	0170-4214 1099-1476