{
  "id": "1407.4834",
  "version": "v2",
  "published": "2014-07-17T20:38:11.000Z",
  "updated": "2014-07-29T14:35:46.000Z",
  "title": "Dimensional estimates for singular sets in geometric variational problems with free boundaries",
  "authors": [
    "Guido De Philippis",
    "Francesco Maggi"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are $\\mathcal H ^{n-3}$-negligible, where $n$ is the ambient space dimension. In particular our results apply to capillarity type problems, and establish everywhere regularity in the three-dimensional case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-29T14:35:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular sets",
      "free boundaries",
      "dimensional estimates",
      "anisotropic geometric variational problems",
      "capillarity type problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4834D"
    }
  }
}