{
  "id": "0905.1685",
  "version": "v1",
  "published": "2009-05-11T21:44:57.000Z",
  "updated": "2009-05-11T21:44:57.000Z",
  "title": "$C^{1,\\al}$ regularity of solutions to parabolic Monge-Ampére equations",
  "authors": [
    "Panagiota Daskalopoulos",
    "Ovidiu Savin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study interior $C^{1, \\al}$ regularity of viscosity solutions of the parabolic Monge-Amp\\'ere equation $$u_t = b(x,t) \\ddua,$$ with exponent $p >0$ and with coefficients $b$ which are bounded and measurable. We show that when $p$ is less than the critical power $\\frac{1}{n-2}$ then solutions become instantly $C^{1, \\al}$ in the interior. Also, we prove the same result for any power $p>0$ at those points where either the solution separates from the initial data, or where the initial data is $C^{1, \\beta}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-11T21:44:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic monge-ampére equations",
      "regularity",
      "initial data",
      "parabolic monge-ampere equation",
      "viscosity solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1685D"
    }
  }
}