{
  "id": "1710.07506",
  "version": "v1",
  "published": "2017-10-20T12:33:06.000Z",
  "updated": "2017-10-20T12:33:06.000Z",
  "title": "Remarks on regularity for $p$-Laplacian type equations in non-divergence form",
  "authors": [
    "Amal Attouchi",
    "Eero Ruosteenoja"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\\gamma\\left(\\Delta u+(p-2)\\Delta_\\infty^N u\\right)=f\\ \\ \\ \\ \\text{in}\\ \\ \\ \\Omega.$$ We investigate local $C^{1,\\alpha}$ regularity of viscosity solutions in the full range $\\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\\gamma$ is close to 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-20T12:33:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35B65",
      "35J92"
    ],
    "keywords": [
      "laplacian type equations",
      "non-divergence form",
      "regularity",
      "viscosity solutions",
      "full range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}