Electromagnetic interactions form the foundation of many modern technologies, particularly in communication systems. A key aspect in this context is the propagation and behavior of electromagnetic waves, which are mathematically described by the time-harmonic Maxwell equations. In this setting, a periodic current density with a prescribed frequency is given, and the resulting electromagnetic waves are computed. Since explicit closed-form solutions of the Maxwell equations are rarely available, practical applications typically rely on numerical methods to approximate the solutions.

The quality of such numerical approximations depends strongly on the chosen method, on the prescribed frequency, and on the smoothness properties of the exact solution. In his doctoral thesis, David Wörgötter studies the time-harmonic Maxwell equations with variable coefficients, which, for instance, model the properties of the medium through which the waves propagate. His work focuses in particular on the regularity of the corresponding solutions. He establishes a regularity theory that characterizes the smoothness of these solutions in terms of the geometry of the underlying domain and the given current density, while also explicitly capturing the influence of the frequency. These results provide important analytical tools for the rigorous analysis and evaluation of numerical methods, in particular finite element methods.

The dissertation was reviewed by Jens Markus MELENK (TU Wien), Serge NICAISE (Université Polytechnique Hauts-de-France), and Euan SPENCE (University of Bath). Both the dissertation and the doctoral defense received the highest distinction from all reviewers. David WÖRGÖTTER will remain at the Institute of Analysis and Scientific Computing for some time to continue his research, and we wish him every success in his future work.