{
  "id": "2201.09771",
  "version": "v1",
  "published": "2022-01-24T16:01:10.000Z",
  "updated": "2022-01-24T16:01:10.000Z",
  "title": "Higher differentiability results in the scale of Besov spaces to a class of double-phase obstacle problems",
  "authors": [
    "Antonio Giuseppe Grimaldi",
    "Erica Ipocoana"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the higher fractional differentiability properties of the gradient of the solutions to variational obstacle problems of the form \\begin{gather*} \\min \\biggl\\{ \\int_{\\Omega} F(x,w,Dw) d x \\ : \\ w \\in \\mathcal{K}_{\\psi}(\\Omega) \\biggr\\}, \\end{gather*} with $F$ double phase functional of the form \\begin{equation*} F(x,w,z)=b(x,w)(|z|^p+a(x)|z|^q), \\end{equation*} where $\\Omega$ is a bounded open subset of $\\mathbb{R}^n$, $\\psi \\in W^{1,p}(\\Omega)$ is a fixed function called \\textit{obstacle} and $\\mathcal{K}_{\\psi}(\\Omega)= \\{ w \\in W^{1,p}(\\Omega) : w \\geq \\psi \\ \\text{a.e. in} \\ \\Omega \\}$ is the class of admissible functions. Assuming that the gradient of the obstacle belongs to a suitable Besov space, we are able to prove that the gradient of the solution preserves some fractional differentiability property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-24T16:01:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A27",
      "49J40",
      "47J20"
    ],
    "keywords": [
      "higher differentiability results",
      "double-phase obstacle problems",
      "besov space",
      "fractional differentiability property",
      "higher fractional differentiability properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}