{
  "id": "0907.2882",
  "version": "v1",
  "published": "2009-07-16T16:47:39.000Z",
  "updated": "2009-07-16T16:47:39.000Z",
  "title": "The stability for the Cauchy problem for elliptic equations",
  "authors": [
    "Giovanni Alessandrini",
    "Luca Rondi",
    "Edi Rosset",
    "Sergio Vessella"
  ],
  "comment": "57 pages, review article",
  "journal": "Inverse Problems 25 123004, 2009, (47pp)",
  "doi": "10.1088/0266-5611/25/12/123004",
  "categories": [
    "math.AP"
  ],
  "abstract": "We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-16T16:47:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R25",
      "35B60",
      "35R30",
      "31A15",
      "30C62",
      "30G20"
    ],
    "keywords": [
      "elliptic equations",
      "essentially optimal stability results",
      "inverse boundary value problems",
      "wide generality",
      "ill-posed cauchy problem"
    ],
    "tags": [
      "review article",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009InvPr..25l3004A"
    }
  }
}