Transmission problems for Maxwells equations with weakly Lipschitz interfaces

We prove sufficient conditions on material constants, frequency and Lipschitz regularity of interface for well posedness of a generalized Maxwell transmission problem in finite energy norms. This is done by embedding Maxwellʹs equations in an elliptic Dirac equation, by constructing the natural trace space for the transmission problem and using Hodge decompositions for operators d and (delta)on weakly Lipschitz domains to prove stability. We also obtain results for boundary value problems and transmission problems for the Hodge-Dirac equation and prove spectral estimates for boundary singular integral operators related to double layer potentials.