{
  "id": "1407.4616",
  "version": "v1",
  "published": "2014-07-17T10:04:15.000Z",
  "updated": "2014-07-17T10:04:15.000Z",
  "title": "Conditional stability for backward parabolic equations with $\\rm{Log}\\rm{Lip}_t \\times \\rm{Lip}_x$-coefficients",
  "authors": [
    "D. Del Santo",
    "Ch. P. Jäh",
    "M. Prizzi"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we present an improvement of [Math. Ann. 345 (2009), 213--243], where the authors proved a result concerning continuous dependence for backward parabolic operators whose coefficients are Log-Lipschitz in $t$ and $C^2$ in $x$. The $C^2$ regularity with respect to $x$ had to be assumed for technical reasons. Here we remove this assumption, replacing it with Lipschitz-continuity. The main tools in the proof are Littlewood-Paley theory and Bony's paraproduct as well as a result of Coifman and Meyer [Ast\\'erisque 57, 1978, Th. 35].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-17T10:04:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B30",
      "34A12",
      "35A02"
    ],
    "keywords": [
      "backward parabolic equations",
      "conditional stability",
      "coefficients",
      "result concerning continuous dependence",
      "backward parabolic operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4616D"
    }
  }
}