THE NULL-TIME-LIKE BOUNDARY-PROBLEM FOR MAXWELLS EQUATIONS IN MINKOWSKI SPACE

We consider Maxwell's equations in an exterior region of Minkowski spa ce, with boundary conditions specified on a timelike cylinder and on a characteristic cone. We prove gauge fixing results and uniqueness and existence results which lead us to introduce two classes of gauge-red uced boundary data, which have the property that there is a one-one co rrespondence between boundary data in each class and the gauge-equival ence classes of solutions of Maxwell's equations in the exterior regio n. These classes of boundary data provide constraint-free parametrizat ions of the space of all solutions of Maxwell's equations.