{
  "id": "1908.10889",
  "version": "v1",
  "published": "2019-08-28T18:04:41.000Z",
  "updated": "2019-08-28T18:04:41.000Z",
  "title": "Regularity of Minimizers of a Tensor-valued Variational Obstacle Problem in Three Dimensions",
  "authors": [
    "Zhiyuan Geng",
    "Jiajun Tong"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Motivated by Ball and Majumdar's modification of Landau-de Gennes model for nematic liquid crystals, we study energy-minimizer $Q$ of a tensor-valued variational obstacle problem in a bounded 3-D domain with prescribed boundary data. The energy functional is designed to blow up as $Q$ approaches the obstacle. Under certain assumptions, especially on blow-up profile of the singular bulk potential, we prove higher interior regularity of $Q$, and show that the contact set of $Q$ is either empty, or small with characterization of its Hausdorff dimension. We also prove boundary partial regularity of the energy-minimizer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-28T18:04:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J50",
      "35J47",
      "82D30"
    ],
    "keywords": [
      "tensor-valued variational obstacle problem",
      "minimizers",
      "boundary partial regularity",
      "landau-de gennes model",
      "higher interior regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}