{
  "id": "1706.06928",
  "version": "v1",
  "published": "2017-06-21T14:25:16.000Z",
  "updated": "2017-06-21T14:25:16.000Z",
  "title": "The best constant in the embedding of $W^{N,1}({\\mathbb R}^N)$ into $L^\\infty({\\mathbb R}^N)$",
  "authors": [
    "Itai Shafrir"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We compute the best constant in the embedding of $W^{N,1}({\\mathbb R}^N)$ into $L^\\infty({\\mathbb R}^N)$, extending a result of Humbert and Nazaret in dimensions one and two to any $N$. The main tool is the identification of $\\log |x|$ as a fundamental solution of a certain elliptic operator of order $2N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-21T14:25:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "35A23"
    ],
    "keywords": [
      "best constant",
      "elliptic operator",
      "fundamental solution",
      "main tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}