{
  "id": "1811.01599",
  "version": "v1",
  "published": "2018-11-05T10:44:18.000Z",
  "updated": "2018-11-05T10:44:18.000Z",
  "title": "Radial symmetry for a quasilinear elliptic equation with a critical Sobolev growth and Hardy potential",
  "authors": [
    "Francescantonio Oliva",
    "Berardino Sciunzi",
    "Giusi Vaira"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider weak positive solutions to the critical $p$-Laplace equation with Hardy potential in $\\mathbb R^N$ $$-\\Delta_p u -\\frac{\\gamma}{|x|^p} u^{p-1}=u^{p^*-1}$$ where $1<p<N$, $0\\le \\gamma <\\left(\\frac{N-p}{p}\\right)^p$ and $p^*=\\frac{Np}{N-p}$. The main result is to show that all the solutions in $\\mathcal D^{1, p}(\\mathbb R^N)$ are radial and radially decreasing about the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T10:44:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasilinear elliptic equation",
      "critical sobolev growth",
      "hardy potential",
      "radial symmetry",
      "weak positive solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}