{
  "id": "2104.06673",
  "version": "v1",
  "published": "2021-04-14T07:35:46.000Z",
  "updated": "2021-04-14T07:35:46.000Z",
  "title": "BV and Sobolev homeomorphisms between metric measure spaces and the plane",
  "authors": [
    "Camillo Brena",
    "Daniel Campbell"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that given a homeomorphism $f:G\\rightarrow\\Omega$ where $G$ is a open subset of $\\mathbb{R}^2$ and $\\Omega$ is a open subset of a $2$-Ahlfors regular metric measure space supporting a weak $(1,1)$-Poincar\\'e inequality, it holds $f\\in BV_{\\operatorname{loc}}(G,\\Omega)$ if and only $f^{-1}\\in BV_{\\operatorname{loc}}(\\Omega,G)$. Further if $f$ satisfies the Luzin N and N$^{-1}$ conditions then $f\\in W^{1,1}_{\\operatorname{loc}}(G,\\Omega)$ if and only if $f^{-1}\\in W^{1,1}_{\\operatorname{loc}}(\\Omega,G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-14T07:35:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "30L99"
    ],
    "keywords": [
      "sobolev homeomorphisms",
      "ahlfors regular metric measure space",
      "open subset",
      "regular metric measure space supporting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}