The largest essential spectrum \(\sigma _{e5}\) of a transmission problem for the dissipative Maxwell system through a semi-transparent Faraday layer \(\Sigma \) consists of the union of the Weyl essential spectra of a Maxwell operator with homogeneous boundary conditions and a carefully defined ’extended’ essential spectrum of a pseudodifferential operator of order 0 on \(\Sigma \) . However, only partial information is available regarding \(\sigma _{e4}\) . A natural question is then to clarify whether \(\sigma _{e4} = \sigma _{e5}\) . The open problem is to prove or disprove the existence of open disks of eigenvalues.
