{
  "id": "1501.03005",
  "version": "v1",
  "published": "2015-01-13T13:57:19.000Z",
  "updated": "2015-01-13T13:57:19.000Z",
  "title": "Quantitative estimates on Jacobians for hybrid inverse problems",
  "authors": [
    "Giovanni Alessandrini",
    "Vincenzo Nesi"
  ],
  "comment": "15 pages, submitted",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider $\\sigma$-harmonic mappings, that is mappings $U$ whose components $u_i$ solve a divergence structure elliptic equation ${\\rm div} (\\sigma \\nabla u_i)=0$, for $i=1,\\ldots,n $. We investigate whether, with suitably prescribed Dirichlet data, the Jacobian determinant can be bounded away from zero. Results of this sort are required in the treatment of the so-called hybrid inverse problems, and also in the field of homogenization studying bounds for the effective properties of composite materials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-13T13:57:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C62",
      "35J55"
    ],
    "keywords": [
      "hybrid inverse problems",
      "quantitative estimates",
      "divergence structure elliptic equation",
      "suitably prescribed dirichlet data",
      "jacobian determinant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150103005A"
    }
  }
}