{
  "id": "1405.6612",
  "version": "v2",
  "published": "2014-05-26T15:24:04.000Z",
  "updated": "2014-06-24T10:24:45.000Z",
  "title": "Hölder estimates for viscosity solutions of equations of fractional $p$-Laplace type",
  "authors": [
    "Erik Lindgren"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove H\\\"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \\text{PV} \\int_{\\mathbb{R}^n}\\frac{|u(x)-u(x+y)|^{p-2}(u(x)-u(x+y))}{|y|^{n+sp}}\\, dy =0, $$ where $s\\in (0,1)$ and $p>2$ or $1/(1-s)<p<2$. Our results also apply for inhomogeneous equations with more general kernels, when $p$ and $s$ are allowed to vary with $x$, without any regularity assumption on $p$ and $s$. This complements and extends some of the recently obtained H\\\"older estimates for weak solutions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-24T10:24:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solutions",
      "hölder estimates",
      "laplace type",
      "fractional",
      "general kernels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6612L"
    }
  }
}