{
  "id": "2106.00439",
  "version": "v1",
  "published": "2021-06-01T12:35:31.000Z",
  "updated": "2021-06-01T12:35:31.000Z",
  "title": "Regularity of flat free boundaries for a $p(x)$-Laplacian problem with right hand side",
  "authors": [
    "Fausto Ferrari",
    "Claudia Lederman"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:0912.2057 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider viscosity solutions to a one-phase free boundary problem for the $p(x)$-Laplacian with non-zero right hand side. We apply the tools developed in \\cite{D} to prove that flat free boundaries are $C^{1,\\alpha}$. Moreover, we obtain some new results for the operator under consideration that are of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-01T12:35:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "35R35",
      "35B65",
      "35J60",
      "35J70"
    ],
    "keywords": [
      "flat free boundaries",
      "laplacian problem",
      "non-zero right hand side",
      "one-phase free boundary problem",
      "regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}