{
  "id": "2003.04037",
  "version": "v1",
  "published": "2020-03-09T10:59:09.000Z",
  "updated": "2020-03-09T10:59:09.000Z",
  "title": "Sharp gradient stability for the Sobolev inequality",
  "authors": [
    "Alessio Figalli",
    "Yi Ru-Ya Zhang"
  ],
  "comment": "32 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p<2$, while it depends on $p$ for $p>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-09T10:59:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "26D10"
    ],
    "keywords": [
      "sharp gradient stability",
      "sobolev inequality",
      "sharp quantitative version",
      "optimal functions",
      "sharp exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}