{
  "id": "2208.14791",
  "version": "v1",
  "published": "2022-08-31T12:14:25.000Z",
  "updated": "2022-08-31T12:14:25.000Z",
  "title": "Regularity theory for fully nonlinear parabolic obstacle problems",
  "authors": [
    "Alessandro Audrito",
    "Teo Kukuljan"
  ],
  "comment": "44 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part: near regular points the free boundary is $C^\\infty$ in space and time. Furthermore, we prove that the set of singular points is locally covered by a Lipschitz manifold of dimension $n-1$ which is also $\\varepsilon$-flat in space, for any $\\varepsilon>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T12:14:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "35K55",
      "35B44",
      "35B65"
    ],
    "keywords": [
      "fully nonlinear parabolic obstacle problems",
      "regularity theory",
      "free boundary splits",
      "singular part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}