Quantitative Trace Estimates for the Maxwell system in Lipschitz Domains

TL;DR

This paper develops quantitative estimates for the Maxwell system in Lipschitz domains, emphasizing trace and extension operators, and provides explicit bounds for interior scattering problems based on domain geometry.

Contribution

It introduces new quantitative estimates that explicitly depend on the Lipschitz character of the domain for the Maxwell system, including trace and extension operators and bounds for scattering solutions.

Findings

Explicit bounds for interior scattering solutions in Lipschitz domains.

Dependence of estimates on the Lipschitz character of the domain.

Weak formulation of the interior scattering problem using the Calderón operator.

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 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.