Maxwell operator in a cylinder with coefficients that do not depend on the longitudinal variable
Nikolai Dmitrievich Filonov · St Petersburg Mathematical Journal · 2019
The Maxwell operator in a 3-dimensional cylinder with Lipschitz cross-section is considered. The coefficients are assumed to be independent of the longitudinal variable. The spectrum of the operator is shown to be absolutely continuous. If the cross-section of the cylinder is multiply connected, then the spectrum fills the real axes. If the cross-section is simply connected, then the spectrum has one gap centered at the origin.