Maxwell's equations with mixed impedance boundary conditions

2025/10/16 by Ben Schweizer, Schweizer, Ben, David Wiedemann +1
Computer Science · Engineering · Mathematics · #35A01 #35Q61 #78A25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2510.14600

openalex publication_date 2025/10/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

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.

Citations

• On polarization interface conditions for time-harmonic Maxwell's equations
• Interface conditions for Maxwell's equations by homogenization of thin inclusions: transmission, reflection or polarization

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