{
  "id": "2209.05976",
  "version": "v1",
  "published": "2022-09-13T13:19:06.000Z",
  "updated": "2022-09-13T13:19:06.000Z",
  "title": "Local boundedness for $p$-Laplacian with degenerate coefficients",
  "authors": [
    "Peter Bella",
    "Mathias Schäffner"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study local boundedness for subsolutions of nonlinear nonuniformly elliptic equations whose prototype is given by $\\nabla \\cdot (\\lambda |\\nabla u|^{p-2}\\nabla u)=0$, where the variable coefficient $0\\leq\\lambda$ and its inverse $\\lambda^{-1}$ are allowed to be unbounded. Assuming certain integrability conditions on $\\lambda$ and $\\lambda^{-1}$ depending on $p$ and the dimension, we show local boundedness. Moreover, we provide counterexamples to regularity showing that the integrability conditions are optimal for every $p>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-13T13:19:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "degenerate coefficients",
      "integrability conditions",
      "study local boundedness",
      "nonlinear nonuniformly elliptic equations",
      "variable coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}