{
  "id": "2107.04336",
  "version": "v1",
  "published": "2021-07-09T10:08:06.000Z",
  "updated": "2021-07-09T10:08:06.000Z",
  "title": "Higher differentiability of solutions for a class of obstacle problems with variable exponents",
  "authors": [
    "Niccolò Foralli",
    "Giovanni Giliberti"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove a higher differentiability result for the solutions to a class of obstacle problems in the form \\begin{equation*} \\label{obst-def0} \\min\\left\\{\\int_\\Omega F(x,Dw) dx : w\\in \\mathcal{K}_{\\psi}(\\Omega)\\right\\} \\end{equation*} where $\\psi\\in W^{1,p(x)}(\\Omega)$ is a fixed function called obstacle and $\\mathcal{K}_{\\psi}=\\{w \\in W^{1,p(x)}_{0}(\\Omega)+u_0: w \\ge \\psi \\,\\, \\textnormal{a.e. in $\\Omega$}\\}$ is the class of the admissible functions, for a suitable boundary value $ u_0 $. We deal with a convex integrand $F$ which satisfies the $p(x)$-growth conditions \\begin{equation*}\\label{growth}|\\xi|^{p(x)}\\le F(x,\\xi)\\le C(1+|\\xi|^{p(x)}),\\quad p(x)>1 \\end{equation*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-09T10:08:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "obstacle problems",
      "variable exponents",
      "higher differentiability result",
      "suitable boundary value",
      "convex integrand"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}