Boundary regularity for Maxwellʹs equations with applications to shape optimization

The dynamic Maxwell equations with a strictly dissipative boundary condition is considered. Sharp trace regularity for the electric and the magnetic field are established for both: weak and differentiable solutions. As an application a shape optimization problem for Maxwellʹs equations is considered. In order to characterize the shape derivative as a solution to a boundary value problem, the aforementioned sharp regularity of the boundary traces is critical.