{
  "id": "math/0502286",
  "version": "v1",
  "published": "2005-02-14T15:35:27.000Z",
  "updated": "2005-02-14T15:35:27.000Z",
  "title": "Improved Rellich inequalities for the polyharmonic operator",
  "authors": [
    "G. Barbatis"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "We prove two improved versions of the Hardy-Rellich inequality for the polyharmonic operator $(-\\Delta)^m$ involving the distance to the boundary. The first involves an infinite series improvement using logarithmic functions, while the second contains $L^2$ norms and involves as a coefficient the volume of the domain. We find explicit constants for these inequalities, and we prove their optimality in the first case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-14T15:35:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "26D10"
    ],
    "keywords": [
      "polyharmonic operator",
      "rellich inequalities",
      "infinite series improvement",
      "hardy-rellich inequality",
      "first case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2286B"
    }
  }
}