{
  "id": "1311.4702",
  "version": "v2",
  "published": "2013-11-19T11:31:32.000Z",
  "updated": "2014-05-20T13:45:35.000Z",
  "title": "Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation",
  "authors": [
    "Nikolaos Roidos",
    "Elmar Schrohe"
  ],
  "comment": "21 pages",
  "journal": "J. Differential Equations 257, 611-637 (2014)",
  "categories": [
    "math.AP"
  ],
  "abstract": "Extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted $L^p$-spaces $\\mathcal{H}^{0,\\gamma}_p(\\mathbb{B})$ over a manifold with conical singularities, we show how the same assumptions also yield the existence of bounded imaginary powers on higher order Mellin-Sobolev spaces $\\mathcal{H}^{s,\\gamma}_p(\\mathbb{B})$, $s\\geq0$. As an application we then consider the Cahn-Hilliard equation on a manifold with (possibly warped) conical singularities. Relying on our work for the case of straight cones, we first establish $R$-sectoriality (and thus maximal regularity) for the linearized equation and then deduce the existence of a short time solution with the help of a theorem by Cl\\'ement and Li. We also obtain the short time asymptotics of the solution near the conical point.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-20T13:45:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70",
      "35K59",
      "58J40"
    ],
    "keywords": [
      "higher order mellin-sobolev spaces",
      "bounded imaginary powers",
      "cone differential operators",
      "cahn-hilliard equation",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4702R"
    }
  }
}