{
  "id": "2004.02368",
  "version": "v1",
  "published": "2020-04-06T01:33:07.000Z",
  "updated": "2020-04-06T01:33:07.000Z",
  "title": "BMO and Elasticity: Korn's Inequality; Local Uniqueness in Tension",
  "authors": [
    "Daniel E. Spector",
    "Scott J. Spector"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this manuscript two $BMO$ estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the $BMO$-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the $BMO$-seminorm of the symmetric part of its gradient, that is, a Korn inequality in $BMO$. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a $BMO$-neighborhood in strain space where there are no other equilibrium solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-06T01:33:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74B20",
      "35A02",
      "74G30",
      "42B37",
      "35J57"
    ],
    "keywords": [
      "korns inequality",
      "local uniqueness",
      "equilibrium solution",
      "strain space",
      "constant times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}