{
  "id": "1901.09940",
  "version": "v1",
  "published": "2019-01-28T19:01:07.000Z",
  "updated": "2019-01-28T19:01:07.000Z",
  "title": "Singular perturbation of an elastic energy with a singular weight",
  "authors": [
    "Oleksandr Misiats",
    "Ihsan Topaloglu",
    "Daniel Vasiliu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the singular perturbation of an elastic energy with a singular weight. The minimization of this energy results in a multi-scale pattern formation. We derive an energy scaling law in terms of the perturbation parameter and prove that, although one cannot expect periodicity of minimizers, the energy of a minimizer is uniformly distributed across the sample. Finally, following the approach developed by Alberti and M\\\"{u}ller in 2001 we prove that a sequence of minimizers of the perturbed energies converges to a Young measure supported on functions of slope $\\pm 1$ and of period depending on the location in the domain and the weights in the energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-28T19:01:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elastic energy",
      "singular weight",
      "singular perturbation",
      "energy scaling law",
      "perturbation parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}