{
  "id": "1907.08527",
  "version": "v1",
  "published": "2019-07-19T14:30:09.000Z",
  "updated": "2019-07-19T14:30:09.000Z",
  "title": "Regularity results for a class of obstacle problems with $p,q-$growth conditions",
  "authors": [
    "Michele Caselli",
    "Michela Eleuteri",
    "Antonia Passarelli di Napoli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove the local boundedness as well as the local Lipschitz continuity for solutions to a class of obstacle problems of the type $$\\min\\left\\{\\int_\\Omega {F(x, Dz)}: z\\in \\mathcal{K}_{\\psi}(\\Omega)\\right\\}.$$ Here $\\mathcal{K}_{\\psi}(\\Omega)$ is set of admissible functions $z \\in W^{1,p}(\\Omega)$ such that $z \\ge \\psi$ a.e. in $\\Omega$, $\\psi$ being the obstacle and $\\Omega$ being an open bounded set of $\\mathbb{R}^n$, $n \\ge 2$. The main novelty here is that we are assuming $ F(x, Dz)$ satisfying $(p,q)$-growth conditions {and less restrictive assumptions on the obstacle with respect to the existing regularity results}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-19T14:30:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "obstacle problems",
      "growth conditions",
      "local lipschitz continuity",
      "local boundedness",
      "open bounded set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}