Maxwell's equations with mixed impedance boundary conditions
Analysis of PDEs
2025-10-17 v1
Abstract
We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We derive a Fredholm alternative for this system. As a consequence, we obtain the existence of weak solutions for arbitrary sources when the frequency is not a resonance frequency. Our analysis covers the case of singular impedance coefficients.
Keywords
Cite
@article{arxiv.2510.14600,
title = {Maxwell's equations with mixed impedance boundary conditions},
author = {Ben Schweizer and David Wiedemann},
journal= {arXiv preprint arXiv:2510.14600},
year = {2025}
}
Comments
19 pages