{
  "id": "1704.08856",
  "version": "v1",
  "published": "2017-04-28T09:08:00.000Z",
  "updated": "2017-04-28T09:08:00.000Z",
  "title": "Regularity issues for Cosserat continua and $p$-harmonic maps",
  "authors": [
    "Andreas Gastel"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For minimizers in a geometrically nonlinear Cosserat model for micropolar elasticity of continua, we prove interior H\\\"older regularity, up to isolated singular points that may be possible if the exponent $p$ from the model is $2$ or in $(\\frac{32}{15},3)$. The obstacle to full continuity turns out to be the existence of certain minimizing homogeneous $p$-harmonic maps to $S^3$. For those, we slightly improve existing regularity theorems in order to achieve our result on the Cosserat model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-28T09:08:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20",
      "74G40",
      "74B20"
    ],
    "keywords": [
      "harmonic maps",
      "cosserat continua",
      "regularity issues",
      "full continuity turns",
      "geometrically nonlinear cosserat model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}