{
  "id": "1904.02568",
  "version": "v1",
  "published": "2019-04-04T14:13:58.000Z",
  "updated": "2019-04-04T14:13:58.000Z",
  "title": "Rigidity for $p$-Laplacian type equations on compact Riemannian manifolds",
  "authors": [
    "Yu-Zhao Wang",
    "Pei-Can Wei"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we obtain two rigidity results for $p$-Laplacian type equations on compact Riemannian manifolds by using of the carr\\'e du champ and nonlinear flow methods, respectively, where rigidity means that the PDE has only constant solution when a parameter is in a certain range. Moreover, an interpolation inequality is derived as an application.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-04T14:13:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35K92",
      "58J35",
      "53C24"
    ],
    "keywords": [
      "laplacian type equations",
      "compact riemannian manifolds",
      "nonlinear flow methods",
      "rigidity results",
      "interpolation inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}