{
  "id": "2311.02568",
  "version": "v1",
  "published": "2023-11-05T05:22:58.000Z",
  "updated": "2023-11-05T05:22:58.000Z",
  "title": "Nash-Moser iteration approach to gradient estimate and Liouville Property of quasilinear elliptic equations on complete Riemannian manifolds",
  "authors": [
    "Jie He",
    "Jingchen Hu",
    "Youde Wang"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we employ the Nash-Moser iteration technique to analyze the local and global properties of positive solutions to the equation $$\\Delta_pu+a|\\nabla u|^qu^r =0$$on a complete Riemannian manifold with Ricci curvature bounded from below, where $p>1$, $q$, $r$ and $a$ are some real constants. Assuming certain conditions on $a,\\, p,\\, q$ and $r$, we derive a succinct Cheng-Yau type gradient estimate for such solutions. This gradient estimate allows us to obtain a Liouville-type theorem and a Harnack inequality. Our Liouville-type result is novel even in Euclidean space",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-05T05:22:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "35B45",
      "35J92"
    ],
    "keywords": [
      "complete riemannian manifold",
      "nash-moser iteration approach",
      "quasilinear elliptic equations",
      "liouville property",
      "succinct cheng-yau type gradient estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}