{
  "id": "2003.08969",
  "version": "v1",
  "published": "2020-03-19T18:30:04.000Z",
  "updated": "2020-03-19T18:30:04.000Z",
  "title": "A game theoretical approach for an elliptic system with two different operators (the Laplacian and the infinity Laplacian)",
  "authors": [
    "Alfredo Miranda",
    "Julio D Rossi"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "In this paper we find viscosity solutions to an elliptic system governed by two different operators (the Laplacian and the infinity Laplacian) using a probabilistic approach. We analyze a game that combines the Tug-of-War with Random Walks in two different boars. We show that these value functions converge uniformly to a viscosity solution of the elliptic system as the step size goes to zero. In addition, we show uniqueness for the elliptic system using pure PDE techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-19T18:30:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic system",
      "game theoretical approach",
      "infinity laplacian",
      "viscosity solution",
      "pure pde techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}