Propagation of singularities for the wave equation on manifolds with corners
| dc.creator | Vasy, Andras | |
| dc.date | 2004-05-22 | |
| dc.date.accessioned | 2026-07-07T05:08:29Z | |
| dc.date.available | 2026-07-07T05:08:29Z | |
| dc.description | In this paper we describe the propagation of smooth (C^\infty) and Sobolev singularities for the wave equation on smooth manifolds with corners M equipped with a Riemannian metric g. That is, for X=MxR, P=D_t^2-Δ_M, and u locally in H^1 solving Pu=0 with homogeneous Dirichlet or Neumann boundary conditions, we show that the wave front set of u is a union of maximally extended generalized broken bicharacteristics. This result is a smooth counterpart of Lebeau's results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary. Our methods rely on b-microlocal positive commutator estimates, thus providing a new proof for the propagation of singularities at hyperbolic points even if M has a smooth boundary (and no corners). | |
| dc.identifier | https://arxiv.org/abs/math/0405431 | |
| dc.identifier | http://arxiv.org/abs/math/0405431 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71282 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58J47 (Primary) 35L20 (Secondary) | |
| dc.title | Propagation of singularities for the wave equation on manifolds with corners | |
| dc.type | text |