{
  "id": "1403.0428",
  "version": "v2",
  "published": "2014-03-03T13:37:14.000Z",
  "updated": "2014-11-28T10:28:07.000Z",
  "title": "Calderón problem for the p-Laplacian: First order derivative of conductivity on the boundary",
  "authors": [
    "Tommi Brander"
  ],
  "comment": "12 pages. Minor corrections and added references",
  "categories": [
    "math.AP"
  ],
  "abstract": "We recover the gradient of a scalar conductivity defined on a smooth bounded open set in $\\mathbb{R}^d$ from the Dirichlet to Neumann map arising from the $p$-Laplace equation. For any boundary point we recover the gradient using Dirichlet data supported on an arbitrarily small neighbourhood of the boundary point. We use a Rellich-type identity in the proof. Our results are new when $p \\neq 2$. In the $p = 2$ case boundary determination plays a role in several methods for recovering the conductivity in the interior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-03T13:37:14.000Z",
      "title": "Calderón problem for the $p$-Laplacian: First order derivative of conductivity on the boundary",
      "comment": "11 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-28T10:28:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35J92"
    ],
    "keywords": [
      "first order derivative",
      "calderón problem",
      "case boundary determination plays",
      "boundary point",
      "smooth bounded open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.0428B"
    }
  }
}