{
  "id": "1902.05182",
  "version": "v1",
  "published": "2019-02-14T01:48:55.000Z",
  "updated": "2019-02-14T01:48:55.000Z",
  "title": "On reconstruction in the inverse conductivity problem with one measurement",
  "authors": [
    "Masaru Ikehata"
  ],
  "comment": "10 pages",
  "journal": "Inverse Problems, 16(2000), 785-793",
  "doi": "10.1088/0266-5611/16/3/314",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider an inverse problem for electrically conductive material occupying a domain $\\Omega$ in $\\Bbb R^2$. Let $\\gamma$ be the conductivity of $\\Omega$, and $D$ a subdomain of $\\Omega$. We assume that $\\gamma$ is a positive constant $k$ on $D$, $k\\not=1$ and is $1$ on $\\Omega\\setminus D$; both $D$ and $k$ are unknown. The problem is to find a reconstruction formula of $D$ from the Cauchy data on $\\partial\\Omega$ of a non-constant solution $u$ of the equation $\\nabla\\cdot\\gamma\\nabla u=0$ in $\\Omega$. We prove that if $D$ is known to be a convex polygon such that $\\text{diam}\\,D<\\text{dist}\\,(D,\\partial\\Omega)$, there are two formulae for calculating the support function of $D$ from the Cauchy data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-14T01:48:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R05"
    ],
    "keywords": [
      "inverse conductivity problem",
      "measurement",
      "cauchy data",
      "inverse problem",
      "reconstruction formula"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}