{
  "id": "1004.1101",
  "version": "v3",
  "published": "2010-04-07T14:41:41.000Z",
  "updated": "2011-09-15T16:15:37.000Z",
  "title": "Lipschitz continuity of solutions of Poisson equations in metric measure spaces",
  "authors": [
    "Renjin Jiang"
  ],
  "comment": "Potential Analysis, to appear",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $(X,d)$ be a pathwise connected metric space equipped with an Ahlfors $Q$-regular measure $\\mu$, $Q\\in[1,\\infty)$. Suppose that $(X,d,\\mu)$ supports a 2-Poincar\\'e inequality and a Sobolev-Poincar\\'e type inequality for the corresponding \"Gaussian measure\". The author uses the heat equation to study the Lipschitz regularity of solutions of the Poisson equation $\\Delta u=f$, where $f\\in L^p_\\loc$. When $p>Q$, the local Lipschitz continuity of $u$ is established.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-15T16:15:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C25",
      "31B05",
      "35B05",
      "35B45"
    ],
    "keywords": [
      "metric measure spaces",
      "poisson equation",
      "connected metric space",
      "local lipschitz continuity",
      "sobolev-poincare type inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1101J"
    }
  }
}