Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions

We consider Maxwell equations on a smooth domain with per- fectly conducting boundary conditions in isotropic media in two and three dimensions. In the charge-free case we recover Strichartz estimates up to end- points due to Blair–Smith–Sogge for wave equations on domains. For the proof we suitably extend Maxwell equations over the boundary, which intro- duces coefficients on the full space with codimension-1 Lipschitz singularity. We diagonalize this system to half-wave equations amenable to the results of Blair–Smith–Sogge. In case of non-vanishing charges, we quantify the defect to Strichartz estimates for wave equations on domains in terms of the charges.