Propagation of singularities for the wave equation on conic manifolds

Details Propagation of singularities for the wave equation on conic manifolds Propagation of singularities for the wave equation on conic manifolds

2001-11-23

arxiv.org/abs/math/0111255v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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