{
  "id": "2302.03532",
  "version": "v1",
  "published": "2023-02-07T15:25:16.000Z",
  "updated": "2023-02-07T15:25:16.000Z",
  "title": "The asymptotic $p$-Poisson equation as $p \\to \\infty$ in Carnot-Carathéodory spaces",
  "authors": [
    "Luca Capogna",
    "Gianmarco Giovannardi",
    "Andrea Pinamonti",
    "Simone Verzellesi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the asymptotic behavior of solutions to the subelliptic $p$-Poisson equation as $p\\to +\\infty$ in Carnot Carath\\'eodory spaces. In particular, introducing a suitable notion of differentiability, we extend the celebrated result of Bhattacharya, DiBenedetto and Manfredi [Rend. Sem. Mat. Univ. Politec. Torino, 1989, Special Issue, 15-68] and we prove that limits of such solutions solve in the sense of viscosity a hybrid first and second order PDE involving the $\\infty-$Laplacian and the Eikonal equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-07T15:25:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H20",
      "35D40",
      "35J92",
      "35J94"
    ],
    "keywords": [
      "poisson equation",
      "carnot-carathéodory spaces",
      "second order pde",
      "carnot caratheodory spaces",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}