{
  "id": "2410.06230",
  "version": "v1",
  "published": "2024-10-08T17:39:03.000Z",
  "updated": "2024-10-08T17:39:03.000Z",
  "title": "Pointwise Schauder estimates for optimal transport maps of rough densities",
  "authors": [
    "Arghya Rakshit"
  ],
  "comment": "26 pages, 3 figures, comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a pointwise $C^{2,\\,\\alpha}$ estimate for the potential of the optimal transport map in the case that the densities are only close to a constant in a certain $L^p$ sense. To do so we use the variational approach recently developed by Goldman-Otto[ Ann. Sci. \\'Ec. Norm. Sup\\'er.(2020)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-08T17:39:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal transport map",
      "pointwise schauder estimates",
      "rough densities",
      "variational approach",
      "goldman-otto"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}