{
  "id": "1810.01932",
  "version": "v1",
  "published": "2018-10-03T19:47:41.000Z",
  "updated": "2018-10-03T19:47:41.000Z",
  "title": "Segregated configurations involving the square root of the laplacian and their free boundaries",
  "authors": [
    "Daniela De Silva",
    "Susanna Terracini"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the local structure and the regularity of free boundaries of segregated critical configurations involving the square root of the laplacian. We develop an improvement of flatness theory and, as a consequence of this and Almgren's monotonicity formula, we obtain partial regularity (up to a small dimensional set) of the nodal set, thus extending the known resultsfor the standard diffusion to some anomalous case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-03T19:47:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "square root",
      "free boundaries",
      "segregated configurations",
      "almgrens monotonicity formula",
      "small dimensional set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}