{
  "id": "1504.00963",
  "version": "v1",
  "published": "2015-04-04T01:02:51.000Z",
  "updated": "2015-04-04T01:02:51.000Z",
  "title": "$C^{2,α}$ estimates and existence results for certain nonconcave PDE",
  "authors": [
    "Vamsi P. Pingali"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We establish $C^{2,\\alpha}$ estimates for PDE of the form convex $+$ a sum of weakly concave functions of the Hessian, thus generalising a recent result of Collins which is in turn inspired by a theorem of Caffarelli and Yuan. Independently, we also prove an existence result for a certain generalised Monge-Amp\\`ere PDE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-04T01:02:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "existence result",
      "nonconcave pde",
      "form convex",
      "weakly concave functions",
      "caffarelli"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150400963P"
    }
  }
}