{
  "id": "1607.08690",
  "version": "v1",
  "published": "2016-07-29T05:58:17.000Z",
  "updated": "2016-07-29T05:58:17.000Z",
  "title": "The Inverse Problem for the Dirichlet-to-Neumann map on Lorentzian manifolds",
  "authors": [
    "Plamen Stefanov",
    "Yang Yang"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Dirichlet-to-Neumann map $\\Lambda$ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric $g$, a magnetic field $A$ and a potential $q$. We show that we can recover the jet of $g,A,q$ on the boundary form $\\Lambda$ up to a gauge transformation in a stable way. We also show that the lens relation is the canonical relation of $\\Lambda$ away from the diagonal and that the light ray transforms of $A$ and $q$ are recoverable from $\\Lambda$ in a stable way. We present applications for recovery of $A$ and $q$ in a logarithmically stable way, and uniqueness with partial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-29T05:58:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet-to-neumann map",
      "inverse problem",
      "stable way",
      "light ray transforms",
      "wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}