{
  "id": "2101.10740",
  "version": "v1",
  "published": "2021-01-26T12:18:50.000Z",
  "updated": "2021-01-26T12:18:50.000Z",
  "title": "Counterexamples to inverse problems for the wave equation",
  "authors": [
    "Tony Liimatainen",
    "Lauri Oksanen"
  ],
  "comment": "12",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We construct counterexamples to inverse problems for the wave operator on domains in $\\mathbb{R}^{n+1}$, $n \\ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formulated in terms certain restrictions of the Dirichlet-to-Neumann map. The Lorentzian metrics giving counterexamples are time-dependent, but they are smooth and non-degenerate. On $\\mathbb{R}^{n+1}$ the metrics are conformal to the Minkowski metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-26T12:18:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35L05",
      "58J45"
    ],
    "keywords": [
      "inverse problems",
      "wave equation",
      "lorentzian metrics giving counterexamples",
      "non-isometric lorentzian metrics",
      "partial data measurements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}