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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| Abstract | 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. |
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| AbstractList | 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. 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 Calder\'on 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. |
| Author | Stachura, Eric Wellander, Niklas |
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| BackLink | https://doi.org/10.48550/arXiv.2010.01159$$DView paper in arXiv https://doi.org/10.1002/mma.7434$$DView published paper (Access to full text may be restricted) |
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| Copyright | 2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
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| DOI | 10.48550/arxiv.2010.01159 |
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| Snippet | We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the... We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the... |
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| Title | Quantitative Trace Estimates for the Maxwell system in Lipschitz Domains |
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