Local wellposedness of Maxwell systems with retarded material laws on domains with interfaces

We study a Maxwell system on a bounded domain consisting of two sub-domains with different materials, separated by an interface. The nonlinear constitutive relations are nonlocal in time and of a form commonly used in nonlinear optics. We develop a comprehensive local wellposedness theory for solutions belonging to the Sobolev space $\mathcal{H}^k$ on each subdomain, where $k\ge2$ is an integer. The blow-up condition only involves the sup-norm. A main tool are div-curl estimates.