{
  "id": "1408.3568",
  "version": "v2",
  "published": "2014-08-15T15:36:17.000Z",
  "updated": "2015-05-24T14:11:12.000Z",
  "title": "On fractional Laplacians -- 2",
  "authors": [
    "Roberta Musina",
    "Alexander I. Nazarov"
  ],
  "comment": "9 pages; some references are added; a small generalization is given",
  "categories": [
    "math.AP"
  ],
  "abstract": "The present paper is the natural evolution of arXiv:1308.3606. For $s>-1$ we compare two natural types of fractional Laplacians $(-\\Delta)^s$, namely, the \"Navier\" and the \"Dirichlet\" ones. As a main tool, we give the \"dual\" Caffarelli--Silvestre and Stinga--Torrea variational characterizations of these operators for $s\\in(-1,0)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-15T15:36:17.000Z",
      "abstract": "The present paper is the natural evolution of arXiv:1308.3606. For $s>-1$ we compare two natural types of fractional Laplacians $(-\\Delta)^s$, namely, the \"Navier\" and the \"Dirichlet\" ones. As a main tool, we give the \"dual\" Caffarelli--Silvestre and Stinga--Torrea characterizations of these operators for $s\\in(-1,0)$.",
      "comment": "9 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-24T14:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "35A23"
    ],
    "keywords": [
      "fractional laplacians",
      "natural evolution",
      "natural types",
      "main tool",
      "stinga-torrea characterizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.3568M"
    }
  }
}