{
  "id": "1902.04462",
  "version": "v1",
  "published": "2019-02-12T16:04:46.000Z",
  "updated": "2019-02-12T16:04:46.000Z",
  "title": "Stable determination of polygonal inclusions in Calderón's problem by a single partial boundary measurement",
  "authors": [
    "Hongyu Liu",
    "Chun-Hsiang Tsou"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We are concerned with the Calder\\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the support of a convex polygonal inclusion by a single partial boundary measurement. We also derive the uniqueness result in a more general scenario where the conductivities are piecewise constants supported in a nested polygonal geometry. Our methods in establishing the stability and uniqueness results have a significant technical initiative and a strong potential to apply to other inverse boundary value problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-12T16:04:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J25",
      "86A20"
    ],
    "keywords": [
      "single partial boundary measurement",
      "calderóns problem",
      "stable determination",
      "logarithmic type stability estimate",
      "inverse boundary value problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}