{
  "id": "2202.14008",
  "version": "v1",
  "published": "2022-02-28T18:25:57.000Z",
  "updated": "2022-02-28T18:25:57.000Z",
  "title": "The Aronsson Equation for Absolute Minimizers of Supremal Functionals in Carnot-Carathéodory Spaces",
  "authors": [
    "Andrea Pinamonti",
    "Simone Verzellesi",
    "Changyou Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Given a $C^2$ family of vector fields $X_1,...,X_m$ which induces a continuous Carnot-Carath\\'eodory distance, we show that any absolute minimizer of a supremal functional defined by a $C^2$ quasiconvex Hamiltonian $f(x, z, p)$, allowing $z$-variable dependence, is a viscosity solution to the Aronsson equation $-\\langle X(f(x, u(x), Xu(x))), D_p f(x, u(x), Xu(x))\\rangle = 0.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-28T18:25:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supremal functional",
      "aronsson equation",
      "absolute minimizer",
      "carnot-carathéodory spaces",
      "vector fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}