The Calderón operator for time-harmonic Maxwell's equations in closed waveguides

We consider the time-harmonic Maxwell’s equations in a closed, cylindrical waveguide with longitudinal invariant but heterogeneous permittivity and permeability. We consider minimal smoothness assumptions, i.e., the material parameters have to be in $L^{\mathrm{\infty }}$ and the cross section has to be Lipschitz with a possibly non-trivial topology. First, we show that the associated Calderón operator is well-defined and bounded in the natural trace spaces ${\mathbf{H}}_0^{-1\mathrm{/}2}({\mathrm{curl}}_{\mathrm{\Gamma }};\mathrm{\Gamma })\to {\mathbf{H}}_0^{-1\mathrm{/}2}({\mathrm{div}}_{\mathrm{\Gamma }};\mathrm{\Gamma })$. Second, we consider interior Maxwell problems obtained from using the Calderón operator and analyze their well-posedness. Furthermore, we report some additional results on the location and group velocities of the waveguide wavenumbers.