{
  "id": "2212.10807",
  "version": "v1",
  "published": "2022-12-21T06:56:24.000Z",
  "updated": "2022-12-21T06:56:24.000Z",
  "title": "Hölder estimate for a tug-of-war game with $1<p<2$ from Krylov-Safonov regularity theory",
  "authors": [
    "Ángel Arroyo",
    "Mikko Parviainen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We propose a new version of the tug-of-war game and a corresponding dynamic programming principle related to the $p$-Laplacian with $1<p<2$. For this version, the asymptotic H\\\"older continuity of solutions can be directly derived from recent Krylov-Safonov type regularity results in the singular case. Moreover, existence of a measurable solution can be obtained without using boundary corrections. We also establish a comparison principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-21T06:56:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J15",
      "35J92",
      "91A50"
    ],
    "keywords": [
      "krylov-safonov regularity theory",
      "tug-of-war game",
      "hölder estimate",
      "krylov-safonov type regularity results",
      "boundary corrections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}