{
  "id": "1012.4667",
  "version": "v3",
  "published": "2010-12-21T14:20:46.000Z",
  "updated": "2011-03-09T07:31:56.000Z",
  "title": "Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions",
  "authors": [
    "Roman Novikov",
    "Matteo Santacesaria"
  ],
  "journal": "Bulletin des Sciences Math\\'ematiques 135, 5 (2011) 421-434",
  "doi": "10.1016/j.bulsci.2011.04.007",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the multi-channel Gel'fand-Calder\\'on inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation $-\\Delta \\psi + v(x) \\psi = 0$, $x\\in D$, where $v$ is a smooth matrix-valued potential defined on a bounded planar domain $D$. We give an exact global reconstruction method for finding $v$ from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-09T07:31:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-channel gelfand-calderón inverse problem",
      "global uniqueness",
      "dimensions",
      "smooth matrix-valued potential",
      "bounded planar domain"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.4667N"
    }
  }
}