{
  "id": "1103.6184",
  "version": "v1",
  "published": "2011-03-31T13:57:21.000Z",
  "updated": "2011-03-31T13:57:21.000Z",
  "title": "Rellich inequalities with weights",
  "authors": [
    "Paolo Caldiroli",
    "Roberta Musina"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be a cone in $\\mathbb{R}^{n}$ with $n\\ge 2$. For every fixed $\\alpha\\in\\mathbb{R}$ we find the best constant in the Rellich inequality $\\int_{\\Omega}|x|^{\\alpha}|\\Delta u|^{2}dx\\ge C\\int_{\\Omega}|x|^{\\alpha-4}|u|^{2}dx$ for $u\\in C^{2}_{c}(\\bar\\Omega\\setminus\\{0\\})$. We also estimate the best constant for the same inequality on $C^{2}_{c}(\\Omega)$. Moreover we show improved Rellich inequalities with remainder terms involving logarithmic weights on cone-like domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-31T13:57:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "47F05"
    ],
    "keywords": [
      "rellich inequality",
      "best constant",
      "remainder terms",
      "logarithmic weights"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.6184C"
    }
  }
}