{
  "id": "math/0405431",
  "version": "v1",
  "published": "2004-05-22T19:34:37.000Z",
  "updated": "2004-05-22T19:34:37.000Z",
  "title": "Propagation of singularities for the wave equation on manifolds with corners",
  "authors": [
    "Andras Vasy"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "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-\\Delta_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).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-22T19:34:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J47",
      "35L20"
    ],
    "keywords": [
      "wave equation",
      "propagation",
      "extended generalized broken bicharacteristics",
      "wave front set",
      "b-microlocal positive commutator estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5431V"
    }
  }
}