Diffraction at corners for the wave equation on differential forms

Details Diffraction at corners for the wave equation on differential forms Diffraction at corners for the wave equation on differential forms

2009-06-03

arxiv.org/abs/0906.0738v2

Mathematics

Analysis of PDEs

36 pages. Apart from minor changes, a section has been added on other boundary conditions to which the methods of the paper ap

Scientific paper

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.

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