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

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