Maxwell's equations with mixed impedance boundary conditions

Ben Schweizer; David Wiedemann

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arXiv · 2510.14600

Maxwell's equations with mixed impedance boundary conditions

Ben Schweizer·David Wiedemann

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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.

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Ben Schweizer, David Wiedemann. 2025-10-16. Maxwell's equations with mixed impedance boundary conditions. https://arxiv.org/abs/2510.14600

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