{
  "id": "1207.5996",
  "version": "v1",
  "published": "2012-07-25T14:10:36.000Z",
  "updated": "2012-07-25T14:10:36.000Z",
  "title": "Cracks with impedance, stable determination from boundary data",
  "authors": [
    "Giovanni Alessandrini",
    "Eva Sincich"
  ],
  "comment": "40 pages, submitted",
  "journal": "Indiana Univ. Math. J. 62 (2013), 947-989",
  "categories": [
    "math.AP"
  ],
  "abstract": "We discuss the inverse problem of determining the possible presence of an (n-1)-dimensional crack \\Sigma in an n-dimensional body \\Omega with n > 2 when the so-called Dirichlet-to-Neumann map is given on the boundary of \\Omega. In combination with quantitative unique continuation techniques, an optimal single-logarithm stability estimate is proven by using the singular solutions method. Our arguments also apply when the Neumann-to-Dirichlet map or the local versions of the D-N and the N-D map are available.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-25T14:10:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35R25",
      "31B20"
    ],
    "keywords": [
      "boundary data",
      "stable determination",
      "optimal single-logarithm stability estimate",
      "quantitative unique continuation techniques",
      "singular solutions method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5996A"
    }
  }
}