{
  "id": "2003.13437",
  "version": "v1",
  "published": "2020-03-30T13:02:19.000Z",
  "updated": "2020-03-30T13:02:19.000Z",
  "title": "Sobolev mappings and moduli inequalities on Carnot groups",
  "authors": [
    "Evgenii Sevost'yanov",
    "Alexander Ukhlov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In the article we study mappings of Carnot groups satisfy moduli inequalities. We prove that homeomorphisms satisfy the moduli inequalities ($Q$-homeomor\\-phisms) with a locally integrable function $Q$ are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem we prove that mappings inverse to Sobolev homeomorphisms of finite distortion of the class $W^1_{\\nu,\\loc}(\\Omega;\\Omega')$ belong to the Sobolev class $W^1_{1,\\loc}(\\Omega';\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-30T13:02:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C65",
      "22E30",
      "46E35"
    ],
    "keywords": [
      "sobolev mappings",
      "carnot groups satisfy moduli inequalities",
      "weak inverse mapping theorem",
      "sobolev class",
      "homeomorphisms satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}