Regularity theory for nonautonomous Maxwell equations with perfectly conducting boundary conditions

In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity permeability on domains a perfectly conducting boundary. This leads to an initial boundary value problem for first-order hyperbolic system characteristic We prove priori estimates solutions in H m . Moreover, show the existence of unique -solution if coefficients data are sufficiently regular satisfy certain compatibility conditions. Since is system, have exploit divergence conditions order derive energy-type -estimates. A combination these several regularization techniques then yields