{
  "id": "1510.00145",
  "version": "v1",
  "published": "2015-10-01T08:52:37.000Z",
  "updated": "2015-10-01T08:52:37.000Z",
  "title": "Integral representation for functionals defined on $SBD^p$ in dimension two",
  "authors": [
    "Sergio Conti",
    "Matteo Focardi",
    "Flaviana Iurlano"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove an integral representation result for functionals with growth conditions which give coercivity on the space $SBD^p(\\Omega)$, for $\\Omega\\subset\\mathbb{R}^2$. The space $SBD^p$ of functions whose distributional strain is the sum of an $L^p$ part and a bounded measure supported on a set of finite $\\mathcal{H}^{1}$-dimensional measure appears naturally in the study of fracture and damage models. Our result is based on the construction of a local approximation by $W^{1,p}$ functions. We also obtain a generalization of Korn's inequality in the $SBD^p$ setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-01T08:52:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functionals",
      "integral representation result",
      "dimensional measure appears",
      "korns inequality",
      "growth conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000145C"
    }
  }
}