{
  "id": "1511.03248",
  "version": "v1",
  "published": "2015-11-10T20:09:00.000Z",
  "updated": "2015-11-10T20:09:00.000Z",
  "title": "Upper bounds for parabolic equations and the Landau equation",
  "authors": [
    "Luis Silvestre"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a parabolic equation in nondivergence form, defined in the full space $[0,\\infty) \\times \\mathbb R^d$, with a power nonlinearity as the right hand side. We obtain an upper bound for the solution in terms of a weighted control in $L^p$. This upper bound is applied to the homogeneous Landau equation with moderately soft potentials. We obtain an estimate in $L^\\infty(\\mathbb R^d)$ for the solution of the Landau equation, for positive time, which depends only on the mass, energy and entropy of the initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-10T20:09:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B45"
    ],
    "keywords": [
      "upper bound",
      "parabolic equation",
      "right hand side",
      "power nonlinearity",
      "nondivergence form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}