(1) Department of Mathematics, Massachusetts Institute of Technology, 02139 Cambridge, MA, USA;(2) Department of Mathematics, Northwestern University, 60208 Evanston, IL, USA
Abstract:
For the wave equation associated to the Laplacian on a compact manifold with boundary with a conic metric (with respect to which the boundary is metrically a point) the propagation of singularities through the boundary is analyzed. Under appropriate regularity assumptions the diffracted, non-direct, wave produced by the boundary is shown to have Sobolev regularity greater than the incoming wave.