Dr Robert Schippa - Resolvent estimates for time-harmonic Maxwell equations

We prove resolvent estimates for time-harmonic Maxwell equations in L^p-spaces with pointwise, spatially homogeneous, and possibly anisotropic material laws. The resolvent estimates allow for the proof of Limiting Absorption Principles and construction of solutions. In the fully anisotropic case, which is joint work with Rainer Mandel, the construction relies on new Bochner-Riesz estimates with negative index for non-elliptic surfaces. The involved diagonalization argument for Maxwell equations also yields new well-posedness results in the time-dependent case. This is joint work with Roland Schnaubelt.

The talk is based on the preprints arXiv:2103.16951, 2103.17176, 2105.06146.