{
  "id": "1010.2889",
  "version": "v1",
  "published": "2010-10-14T12:39:58.000Z",
  "updated": "2010-10-14T12:39:58.000Z",
  "title": "Local Gradient Estimate for $p$-harmonic functions on Riemannian Manifolds",
  "authors": [
    "Xiaodong Wang",
    "Lei Zhang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "For positive $p$-harmonic functions on Riemannian manifolds, we derive a gradient estimate and Harnack inequality with constants depending only on the lower bound of the Ricci curvature, the dimension $n$, $p$ and the radius of the ball on which the function is defined. Our approach is based on a careful application of the Moser iteration technique and is different from Cheng-Yau's method employed by Kostchwar and Ni, in which a gradient estimate for positive $p$-harmonic functions is derived under the assumption that the sectional curvature is bounded from below.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-14T12:39:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B20",
      "35J15"
    ],
    "keywords": [
      "harmonic functions",
      "local gradient estimate",
      "riemannian manifolds",
      "moser iteration technique",
      "sectional curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.2889W"
    }
  }
}