Diffraction at corners for the wave equation on differential forms

Abstract

In this paper we prove the propagation of singularities for the wave equation on differential forms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds with corners, which in particular includes a formulation of Maxwell's equations. These results are analogous to those obtained by the author for the scalar wave equation and for the wave equation on systems with Dirichlet or Neumann boundary conditions earlier. The main novelty is thus the presence of natural boundary conditions, which effectively make the problem non-scalar, even `to leading order', at corners of codimension at least 2.