{
  "id": "2202.12005",
  "version": "v1",
  "published": "2022-02-24T10:30:42.000Z",
  "updated": "2022-02-24T10:30:42.000Z",
  "title": "On isosupremic vectorial minimisation problems in $L^\\infty$ with general nonlinear constraints",
  "authors": [
    "Ed Clark",
    "Nikos Katzourakis"
  ],
  "comment": "27 pages, 1 table",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We study minimisation problems in $L^\\infty$ for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear operator. Examples of admissible operators include those expressing pointwise, unilateral, integral isoperimetric, elliptic quasilinear differential, jacobian and null Lagrangian constraints. Via the method of $L^p$ approximations as $p\\to \\infty$, we illustrate the existence of a special $L^\\infty$ minimiser which solves a divergence PDE system involving certain auxiliary measures as coefficients. This system can be seen as a divergence form counterpart of the Aronsson PDE system which is associated with the constrained $L^\\infty$ variational problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-24T10:30:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J94",
      "49J20",
      "49K20",
      "49K35",
      "49K99",
      "35J92"
    ],
    "keywords": [
      "isosupremic vectorial minimisation problems",
      "general nonlinear constraints",
      "general quasiconvex first order functionals",
      "pde system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}