{
  "id": "2304.03939",
  "version": "v1",
  "published": "2023-04-08T06:54:57.000Z",
  "updated": "2023-04-08T06:54:57.000Z",
  "title": "Compact contact sets of sub-quadratic solutions to the thin obstacle problem",
  "authors": [
    "Simon Eberle",
    "Hui Yu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact contact set, we show that it must be an ellipsoid.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-08T06:54:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "35B65"
    ],
    "keywords": [
      "compact contact set",
      "thin obstacle problem",
      "sub-quadratic solutions",
      "study global solutions",
      "quadratic growth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}