{
  "id": "1905.11956",
  "version": "v1",
  "published": "2019-05-28T17:25:09.000Z",
  "updated": "2019-05-28T17:25:09.000Z",
  "title": "Almost minimizers for the thin obstacle problem",
  "authors": [
    "Seongmin Jeon",
    "Arshak Petrosyan"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider Anzellotti-type almost minimizers for the thin obstacle (or Signorini) problem with zero thin obstacle and establish their $C^{1,\\beta}$ regularity on the either side of the thin manifold, the optimal growth away from the free boundary, the $C^{1,\\gamma}$ regularity of the regular part of the free boundary, as well as a structural theorem for the singular set. The analysis of the free boundary is based on a successful adaptation of energy methods such as a one-parameter family of Weiss-type monotonicity formulas, Almgren-type frequency formula, and the epiperimetric and logarithmic epiperimetric inequalities for the solutions of the thin obstacle problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-28T17:25:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N60",
      "35R35"
    ],
    "keywords": [
      "thin obstacle problem",
      "free boundary",
      "minimizers",
      "optimal growth away",
      "almgren-type frequency formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}