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 [22 Vasy , A. ( 2008 ). Propagation of singularities for the wave equation on manifolds with corners . Annals of Math. 168 : 749 – 812 .[Crossref] , [Google Scholar]] and for the wave equation on systems with Dirichlet or Neumann boundary conditions in [21 Vasy , A. ( 2008 ). Diffraction by edges . Modern Physics Letters B 22 : 2287 – 2328 .[Crossref], [Web of Science ®] , [Google Scholar]]. 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 ≥2.

Locations

• Communications in Partial Differential Equations - View
• arXiv (Cornell University) - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF