Quasilinear Maxwell equations

Abstract: We show low regularity local well-posedness for Maxwell equations in media. To this end, we show Strichartz estimates for solutions to Maxwell equations withcoefficients of regularity C^2 and lower. The proof is based on a diagonalization with pseudo-differential operators. In two dimensions, in the charge-free case Strichartz estimates for wave equations with rough coefficients are recovered.In three dimensions, we shall see how the dispersive properties change depending on the anisotropy of the permittivity.

The talk is based on joint work with Roland Schnaubelt and Rainer Mandel.