{
  "id": "2209.03011",
  "version": "v1",
  "published": "2022-09-07T09:13:57.000Z",
  "updated": "2022-09-07T09:13:57.000Z",
  "title": "A note on the supersolution method for Hardy's inequality",
  "authors": [
    "Francesca Bianchi",
    "Lorenzo Brasco",
    "Firoj Sk",
    "Anna Chiara Zagati"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We prove a characterization of Hardy's inequality in Sobolev-Slobodecki\\u{\\i} spaces in terms of positive local weak supersolutions of the relevant Euler-Lagrange equation. This extends previous results by Ancona and Kinnunen & Korte for standard Sobolev spaces. The proof is based on variational methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-07T09:13:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hardys inequality",
      "supersolution method",
      "standard sobolev spaces",
      "positive local weak supersolutions",
      "relevant euler-lagrange equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}