{
  "id": "math/0201184",
  "version": "v2",
  "published": "2002-01-20T14:22:08.000Z",
  "updated": "2002-04-23T15:04:21.000Z",
  "title": "Differential Operators on Conic Manifolds: Maximal Regularity and Parabolic Equations",
  "authors": [
    "S. Coriasco",
    "E. Schrohe",
    "J. Seiler"
  ],
  "comment": "18 pages (revised version, 23/04/'02)",
  "journal": "Bull. Soc. Roy. Sci. Li\\`ege 70, fasc. 4-5-6, 207-229 (2001)",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We study an elliptic differential operator A on a manifold with conic points. Assuming A to be defined on the smooth functions supported away from the singularities, we first address the question of possible closed extensions of A to L^p Sobolev spaces and then explain how additional ellipticity conditions ensure maximal regularity for the operator A. Investigating the Lipschitz continuity of the maps f(u)=|u|^\\alpha, with real \\alpha \\ge 1, and f(u)=u^\\alpha, with \\alpha a natural number, and using a result of Cl\\'ement and Li, we finally show unique solvability of a quasilinear equation of the form \\dot{u} - a(u) \\Delta u = f(u) in suitable spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-04-23T15:04:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J40",
      "35K65",
      "47A10"
    ],
    "keywords": [
      "differential operator",
      "conic manifolds",
      "parabolic equations",
      "ellipticity conditions ensure maximal regularity",
      "additional ellipticity conditions ensure maximal"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1184C"
    }
  }
}