{
  "id": "1810.03003",
  "version": "v1",
  "published": "2018-10-06T13:51:31.000Z",
  "updated": "2018-10-06T13:51:31.000Z",
  "title": "Locally invertible $σ$-harmonic mappings",
  "authors": [
    "Giovanni Alessandrini",
    "Vincenzo Nesi"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We extend a classical theorem by H. Lewy to planar $\\sigma$-harmonic mappings, that is mappings $U$ whose components $u^1$ and $u^2$ solve a divergence structure elliptic equation ${\\rm div} (\\sigma \\nabla u^i)=0$ , for $i=1,2$. A similar result is established for pairs of solutions of certain second order non--divergence equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-06T13:51:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C62",
      "35J55"
    ],
    "keywords": [
      "harmonic mappings",
      "locally invertible",
      "second order non-divergence equations",
      "divergence structure elliptic equation",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}