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Quantitative trace estimates for the Maxwell system in Lipschitz domains
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-05-02 , DOI: 10.1002/mma.7434
Eric Stachura 1 , Niklas Wellander 2
Affiliation  

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.

中文翻译:

Lipschitz 域中 Maxwell 系统的定量迹估计

我们为 Lipschitz 域中的各向异性 Maxwell 系统开发了各种定量估计,重点是这些估计如何精确地取决于域的 Lipschitz 特性。我们特别注意某些 Sobolev 空间上的迹运算符和扩展运算符。最后,我们根据外部 Calderón 算子提供了内部散射问题的弱公式,并根据入射场和域的 Lipschitz 特性为内部问题的解决方案提供了明确的界限。
更新日期:2021-05-02
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