{
  "id": "1506.01699",
  "version": "v1",
  "published": "2015-06-04T19:47:08.000Z",
  "updated": "2015-06-04T19:47:08.000Z",
  "title": "Remarks on the Green's function of the linearized Monge-Ampère operator",
  "authors": [
    "Nam Q. Le"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note, we obtain sharp bounds for the Green's function of the linearized Monge-Amp\\`ere operators associated to convex functions with either Hessian determinant bounded away from zero and infinity or Monge-Amp\\`ere measure satisfying a doubling condition. Our result is an affine invariant version of the classical result of Littman-Stampacchia-Weinberger for uniformly elliptic operators in divergence form. We also obtain the $L^{p}$ integrability for the gradient of the Green's function in two dimensions. As an application, we obtain a removable singularity result for the linearized Monge-Amp\\`ere equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-04T19:47:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "greens function",
      "linearized monge-ampère operator",
      "hessian determinant bounded away",
      "affine invariant version",
      "convex functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150601699L"
    }
  }
}