{
  "id": "2004.10287",
  "version": "v1",
  "published": "2020-04-21T20:33:41.000Z",
  "updated": "2020-04-21T20:33:41.000Z",
  "title": "Hidden convexity in a problem of nonlinear elasticity",
  "authors": [
    "Nassif Ghoussoub",
    "Young-Heon Kim",
    "Hugo Lavenant",
    "Aaron Zeff Palmer"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure-valued mappings, which coincides with the original problem under our condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-21T20:33:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hidden convexity",
      "incompressible nonlinear elasticity variational problems",
      "global energy minimizer",
      "dual formulation",
      "convex relaxation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}