{
  "id": "2005.10941",
  "version": "v1",
  "published": "2020-05-21T23:30:41.000Z",
  "updated": "2020-05-21T23:30:41.000Z",
  "title": "Improved regularity for the $p$-Poisson equation",
  "authors": [
    "Edgard A. Pimentel",
    "Giane C. Rampasso",
    "Makson S. Santos"
  ],
  "journal": "Nonlinearity, 33, 3050-3061,2020",
  "doi": "10.1088/1361-6544/ab7d21",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we produce new, optimal, regularity results for the solutions to $p$-Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent $p$, that imports information from a limiting profile driven by the Laplace operator. Our arguments contain a novelty of technical interest, namely a sequential stability result; it connects the solutions to $p$-Poisson equations with harmonic functions, yielding improved regularity for the former. Our findings relate a smallness regime with improved $\\mathcal{C}^{1,1-}$-estimates in the presence of $L^\\infty$-source terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-21T23:30:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J60",
      "35J70",
      "49N60",
      "49J45"
    ],
    "keywords": [
      "poisson equation",
      "smallness regime",
      "delicate approximation method",
      "sequential stability result",
      "regularity results"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}