The time dependent Maxwell system with measurable coefficients in Lipschitz domains

Semigroup theory is employed to study inhomogeneous boundary conditions for the time-dependent Maxwell equations with anisotropic material parameters in a non-smooth domain. Only boundedness and measurability of the coefficients are assumed, and the boundary data is assumed to be time independent. When the material parameters are positive definite, a higher order Sobolev theory is developed for the time-dependent Maxwell system.