{
  "id": "1103.0229",
  "version": "v2",
  "published": "2011-03-01T17:23:00.000Z",
  "updated": "2011-10-13T10:04:52.000Z",
  "title": "Convergence of solutions to the $p$-Laplace evolution equation as $p$ goes to 1",
  "authors": [
    "Jonas M. Tölle"
  ],
  "comment": "11 pp",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We prove that the set of solutions to the parabolic singular $p$-Laplace equation with Dirichlet boundary conditions on a bounded Lipschitz domain $\\Omega$ for all space dimensions is continuous in the parameter $p\\in [1,+\\infty)$ and the initial data. The highly singular limit case p=1 is included. In particular, we show that the solutions $u_p$ converge strongly in $L^2(\\Omega)$, uniformly in time, to the solution $u_1$ of the parabolic 1-Laplace equation as $p\\to 1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-13T10:04:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K67",
      "49J45"
    ],
    "keywords": [
      "laplace evolution equation",
      "convergence",
      "dirichlet boundary conditions",
      "highly singular limit case",
      "space dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0229T"
    }
  }
}