{
  "id": "1408.1620",
  "version": "v1",
  "published": "2014-08-07T15:22:49.000Z",
  "updated": "2014-08-07T15:22:49.000Z",
  "title": "Sharp $L^p$-Moser inequality on Riemannian manifolds",
  "authors": [
    "Marcos Teixeira Alves",
    "Jurandir Ceccon"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider $(M,g)$ a smooth compact Riemannian manifold of dimension $n \\geq 2$ without boundary, $1 < p$ a real parameter and $r = \\frac{p(n + p)}{n}$. This paper concerns the validity of the optimal Moser inequality \\[ \\left(\\int_M |u|^r\\; dv_g \\right)^{\\frac{\\tau}{p}} \\leq \\left( A(p,n)^{\\frac{\\tau}{p}} \\left(\\int_M |\\nabla_g u|^p\\; dv_g\\right)^{\\frac{\\tau}{p}} + B_{opt} \\left(\\int_M |u|^p\\; dv_g\\right)^{\\frac{\\tau}{p}} \\right) \\left( \\int_M |u|^p\\; dv_g \\right)^{\\frac{\\tau}{n}} \\; . \\] This kind of inequality was already studied in the last years in the particular cases $1 < p < n$. Here we solve the case $n \\leq p$ and we introduce one more parameter $1 \\leq \\tau \\leq \\min\\{p,2\\}$. Moreover, we prove the existence of an extremal function for the optimal inequality above.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-07T15:22:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth compact riemannian manifold",
      "optimal moser inequality",
      "optimal inequality",
      "extremal function",
      "real parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.1620T"
    }
  }
}