{
  "id": "1210.5723",
  "version": "v2",
  "published": "2012-10-21T12:42:30.000Z",
  "updated": "2013-04-15T12:30:22.000Z",
  "title": "Hardy inequalities on Riemannian manifolds and applications",
  "authors": [
    "Lorenzo D'Ambrosio",
    "Serena Dipierro"
  ],
  "journal": "Ann. Inst. H. Poincar\\'{e} (C) Anal. Non Lin\\'{e}aire (2013)",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a simple sufficient criteria to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second-order differential operator $\\Delta_{p}u := \\Div(\\abs{\\nabla u}^{p-2}\\nabla u)$. Namely, if $\\rho$ is a nonnegative weight such that $-\\Delta_{p}\\rho\\geq0$, then the Hardy inequality $$c\\int_{M}\\frac{\\abs{u}^{p}}{\\rho^{p}}\\abs{\\nabla \\rho}^{p} dv_{g} \\leq \\int_{M}\\abs{\\nabla u}^{p} dv_{g}, \\quad u\\in\\Cinfinito_{0}(M)$$ holds. We show concrete examples specializing the function $\\rho$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-15T12:30:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hardy inequality",
      "applications",
      "quasilinear second-order differential operator",
      "simple sufficient criteria",
      "concrete examples"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5723D"
    }
  }
}