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 inarXiv.org
Main Authors Stachura, Eric, Wellander, Niklas
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.10.2020
Subjects
Domains
Estimates
Mathematics - Analysis of PDEs
Operators
Sobolev space
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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:2331-8422
DOI:10.48550/arxiv.2010.01159