{
  "id": "1009.2138",
  "version": "v1",
  "published": "2010-09-11T05:41:49.000Z",
  "updated": "2010-09-11T05:41:49.000Z",
  "title": "Radial symmetry and symmetry breaking for some interpolation inequalities",
  "authors": [
    "Jean Dolbeault",
    "Maria J. Esteban",
    "Gabriella Tarantello",
    "Achiles Tertikas"
  ],
  "journal": "Calculus of Variations and Partial Differential Equations 42 (2011) 461-485",
  "categories": [
    "math.AP"
  ],
  "abstract": "We analyze the radial symmetry of extremals for a class of interpolation inequalities known as Caffarelli-Kohn-Nirenberg inequalities, and for a class of weighted logarithmic Hardy inequalities which appear as limiting cases of the first ones. In both classes we show that there exists a continuous surface that splits the set of admissible parameters into a region where extremals are symmetric and a region where symmetry breaking occurs. In previous results, the symmetry breaking region was identified by showing the linear instability of the radial extremals. Here we prove that symmetry can be broken even within the set of parameters where radial extremals correspond to local minima for the variational problem associated with the inequality. For interpolation inequalities, such a symmetry breaking phenomenon is entirely new.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-11T05:41:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inequality",
      "interpolation inequalities",
      "radial symmetry",
      "weighted logarithmic hardy inequalities",
      "radial extremals correspond"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.2138D"
    }
  }
}