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arXiv · 2603.16334

Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions

Jens Markus Melenk·David Wörgötter
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Abstract

We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $Ω$ with an analytic boundary $Γ$, on which we impose impedance boundary conditions. We suppose that the (possibly complex-valued) permeability and permittivity tensor fields $\boldsymbolμ^{-1}$ and $\boldsymbol{\varepsilon}$ are piecewise analytic in $Ω$ and discontinuous only across certain mutually disjoint analytic surfaces inside of $Ω$. We show that under these circumstances, any weak solution of Maxwell's equations is piecewise analytic in $Ω$ and that the growth of its derivatives can be controlled explicitly in the wavenumber $k$.

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Jens Markus Melenk, David Wörgötter. 2026-03-17. Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions. https://arxiv.org/abs/2603.16334

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