{
  "id": "2303.05944",
  "version": "v2",
  "published": "2023-03-10T14:25:52.000Z",
  "updated": "2023-10-01T15:42:19.000Z",
  "title": "Generalised second order vectorial $\\infty$-eigenvalue problems",
  "authors": [
    "Ed Clark",
    "Nikos Katzourakis"
  ],
  "comment": "19 pages, Journal: Proceedings of the Royal Society of Edinburgh A, Mathematics",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the problem of minimising the $L^\\infty$ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^\\infty$ norm of a function of the gradient and the map itself. We assume zeroth and first order Dirichlet boundary data, corresponding to the ``hinged\" and the ``clamped\" cases. By employing the method of $L^p$ approximations, we establish the existence of a special $L^\\infty$ minimiser, which solves a divergence PDE system with measure coefficients as parameters. This is a counterpart of the Aronsson-Euler system corresponding to this constrained variational problem. Furthermore, we establish upper and lower bounds for the eigenvalue.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-10-01T15:42:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P30",
      "35D30",
      "35J94",
      "35P15"
    ],
    "keywords": [
      "generalised second order vectorial",
      "eigenvalue problems",
      "first order dirichlet boundary data",
      "divergence pde system",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}