{
  "id": "1902.05191",
  "version": "v1",
  "published": "2019-02-14T02:14:59.000Z",
  "updated": "2019-02-14T02:14:59.000Z",
  "title": "Extraction formulae for an inverse boundary value problem for the equation $\\nabla\\cdot(σ-iωε)\\nabla u=0$",
  "authors": [
    "Masaru Ikehata"
  ],
  "comment": "11 pages",
  "journal": "Inverse Problems, 18(2002), 1281-1290",
  "doi": "10.1088/0266-5611/18/5/304",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider an inverse boundary value problem for the equation $\\nabla\\cdot(\\sigma-i\\omega\\epsilon)\\nabla u=0$ in a given bounded domain $\\Omega$ at a fixed $\\omega>0$. $\\sigma$ and $\\epsilon$ denote the conductivity and permittivity of the material forming $\\Omega$, respectively. We give some formulae for extracting information about the location of the discontinuity surface of $(\\sigma,\\epsilon)$ from the Dirichlet-to-Neumann map. In order to obtain results we make use of two methods. The first is the enclosure method which is based on a new role of the exponentially growing solutions of the equation for the background material. The second is a generalization of the enclosure method based on a new role of Mittag-Leffler's function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-14T02:14:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R05",
      "35R30"
    ],
    "keywords": [
      "inverse boundary value problem",
      "extraction formulae",
      "enclosure method",
      "discontinuity surface",
      "dirichlet-to-neumann map"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}