{
  "id": "2403.06727",
  "version": "v1",
  "published": "2024-03-11T13:45:55.000Z",
  "updated": "2024-03-11T13:45:55.000Z",
  "title": "Minimisers of supremal functionals and mass-minimising 1-currents",
  "authors": [
    "Nikos Katzourakis",
    "Roger Moser"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study vector-valued functions that minimise the $L^\\infty$-norm of their derivatives for prescribed boundary data. We construct a vector-valued, mass minimising $1$-current (i.e., a generalised geodesic) in the domain such that all solutions of the problem coincide on its support. Furthermore, this current can be interpreted as a streamline of the solutions. It also has maximal support among all $1$-currents with certain properties. The construction relies on a $p$-harmonic approximation. In the case of scalar-valued functions, it is closely related to a construction of Evans and Yu. We therefore obtain an extension of their theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-11T13:45:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supremal functionals",
      "minimisers",
      "problem coincide",
      "study vector-valued functions",
      "mass-minimising"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}