Boundary Value Problems for the Bi-Anisotropic Maxwell System in Lipschitz Domains

The initial boundary value problem for the time dependent Maxwell system under bi-anisotropy in a non-smooth domain (a cavity) is analyzed. It is shown that this problem is well-posed provided the material parameters satisfy certain coercivity assumptions. Minimal smoothness of these parameters and time independent boundary data belonging to an appropriate Sobolev space is imposed to obtain existence of classical solutions. Finally, we address the free space problem.