{
  "id": "1812.07779",
  "version": "v1",
  "published": "2018-12-19T06:51:40.000Z",
  "updated": "2018-12-19T06:51:40.000Z",
  "title": "Hölder Continuity and Differentiability Almost Everywhere of $(K_1, K_2)$-Quasiregular Mappings",
  "authors": [
    "Hongya Gao",
    "Chao Liu",
    "Junwei Li"
  ],
  "comment": "This is an English version of our published Chinese article. The Chinese version can be found and downloaded at http://123.57.41.99/Jwk_sxxb_cn//CN/article/downloadArticleFile.do?attachType=PDF&id=21741",
  "journal": "Acta Mathematica Sinica Chinese Series, 2012,55(4), 721-726. http://www.actamath.com/Jwk_sxxb_cn/CN/abstract/abstract21741.shtml",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with $(K_1, K_2)$-quasiregular mappings. It is shown, by Morrey's Lemma and isoperimetric inequality, that every $(K_1, K_2)$-quasiregular mapping satisfies a H\\\"oolder condition with exponent {\\alpha} on compact subsets of its domain, where \\begin{align} \\alpha=\\begin{cases} 1/K_1, & \\text{for } K_1>1, \\\\ \\text{any positive number less than } 1, & \\text{for } K_1=1 \\text{ and } K_2>0, \\\\ 1, & \\text{for } K_1=1 \\text{ and } K_2=0, \\\\ 1, & \\text{for } K_1<1,\\\\ \\end{cases} \\end{align} Differentiability almost everywhere of $(K_1, K_2)$-quasiregular mappings is also derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-19T06:51:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hölder continuity",
      "differentiability",
      "paper deals",
      "morreys lemma",
      "quasiregular mapping satisfies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}