{
  "id": "0711.0591",
  "version": "v2",
  "published": "2007-11-05T13:53:46.000Z",
  "updated": "2008-04-24T08:25:24.000Z",
  "title": "Dimensional reduction for energies with linear growth involving the bending moment",
  "authors": [
    "Jean-Francois Babadjian",
    "Elvira Zappale",
    "Hamdi Zorgati"
  ],
  "comment": "26 pages",
  "journal": "Journal de Math\\'ematiques Pures et Appliqu\\'ees 90, no. 6, (2008), 520-549",
  "categories": [
    "math.AP"
  ],
  "abstract": "A $\\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-24T08:25:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "49Q20",
      "74K35"
    ],
    "keywords": [
      "linear growth",
      "bending moment",
      "dimensional reduction",
      "3d-2d dimension reduction",
      "nonlinear membrane model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.0591B"
    }
  }
}