{
  "id": "2401.13116",
  "version": "v1",
  "published": "2024-01-23T21:51:58.000Z",
  "updated": "2024-01-23T21:51:58.000Z",
  "title": "Sharp second-order regularity for widely degenerate elliptic equations",
  "authors": [
    "Pasquale Ambrosio",
    "Antonio Giuseppe Grimaldi",
    "Antonia Passarelli di Napoli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider local weak solutions of widely degenerate or singular elliptic PDEs of the type \\begin{equation*} -\\,\\mathrm{div}\\left((\\vert Du\\vert-\\lambda)_{+}^{p-1}\\frac{Du}{\\vert Du\\vert}\\right)=f \\,\\,\\,\\,\\,\\,\\, \\text{in}\\,\\,\\Omega, \\end{equation*} where $\\Omega$ is an open subset of $\\mathbb{R}^{n}$ for $n\\geq2$, $\\lambda$ is a positive constant and $(\\,\\cdot\\,)_{+}$ stands for the positive part. We establish some higher differentiability results, under essentially sharp conditions on the datum $f$. Our results improve the one contained in [8] for $\\lambda=0$ and $p>2$, and give back a result similar to that in [12] for $1 < p \\le 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-23T21:51:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70",
      "35J75",
      "35J92",
      "49K20"
    ],
    "keywords": [
      "degenerate elliptic equations",
      "sharp second-order regularity",
      "local weak solutions",
      "singular elliptic pdes",
      "higher differentiability results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}