{
  "id": "1203.1650",
  "version": "v2",
  "published": "2012-03-07T22:31:26.000Z",
  "updated": "2012-11-28T15:59:05.000Z",
  "title": "Lipschitz stability of an inverse boundary value problem for a Schrödinger type equation",
  "authors": [
    "Elena Beretta",
    "Maarten V. de Hoop",
    "Lingyun Qiu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the inverse boundary value problem of determining the potential in the Schr\\\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type. In this work, a Lipschitz type stability is established assuming a priori that the potential is piecewise constant with a bounded known number of unknown values.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-28T15:59:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J57"
    ],
    "keywords": [
      "inverse boundary value problem",
      "schrödinger type equation",
      "lipschitz stability",
      "lipschitz type stability",
      "optimal stability estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.1650B"
    }
  }
}