{
  "id": "0812.0229",
  "version": "v3",
  "published": "2008-12-01T15:03:37.000Z",
  "updated": "2009-06-10T13:09:09.000Z",
  "title": "Monotonicity theorems for Laplace Beltrami operator on Riemannian manifolds",
  "authors": [
    "Eduardo V Teixeira",
    "Lei Zhang"
  ],
  "comment": "21 Pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "For free boundary problems on Euclidean spaces, the monotonicity formulas of Alt-Caffarelli-Friedman and Caffarelli-Jerison-Kenig are cornerstones for the regularity theory as well as the existence theory. In this article we establish the analogs of these results for the Laplace-Beltrami operator on Riemannian manifolds. As an application we show that our monotonicity theorems can be employed to prove the Lipschitz continuity for the solutions of a general class of two-phase free boundary problems on Riemannian manifolds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-06-10T13:09:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "35B65",
      "35J05"
    ],
    "keywords": [
      "laplace beltrami operator",
      "riemannian manifolds",
      "monotonicity theorems",
      "two-phase free boundary problems",
      "monotonicity formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.0229T"
    }
  }
}