{
  "id": "1809.06821",
  "version": "v1",
  "published": "2018-09-18T16:35:25.000Z",
  "updated": "2018-09-18T16:35:25.000Z",
  "title": "Fully nonlinear integro-differential equations with deforming kernels",
  "authors": [
    "Luis Caffarelli",
    "Rafayel Teymurazyan",
    "José Miguel Urbano"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge-Amp\\`{e}re equation. We prove an ABP estimate and a Harnack inequality and derive H\\\"{o}lder and $C^{1,\\alpha}$ regularity results for solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-18T16:35:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fully nonlinear integro-differential equations",
      "deforming kernels",
      "regularity results",
      "regularity theory",
      "abp estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}