Energy conserving boundary conditions for Maxwell's equations in nonhomogeneous medium (Q1819606)

The boundary conditions for the electromagnetic field can be discussed in terms of the energy balance. By physical reasons it is possible that there is no energy transport across the surface even for nonhomogeneous boundary conditions. In the paper presented here the problem of the electromagnetic field in a nonhomogeneous isotropic linear material with energy conserving boundary conditions is proved to be well-posed. For this purpose an inequality relating suitable weighted norms of the sought field and the given sources (or currents) in the spacial domain and at the surface is derived. The estimate is executed immediately for the simplified problem of the half space.