{
  "abstract": "We establish gradient potential estimates for solutions obtained as limits of approximations (SOLA) to the fractional $p$-Laplace equation with finite signed Radon measure data. Under the assumptions $n\\ge2$, $p>2$, $0<s<1$, and $sp>p-1$, every SOLA belongs to $W^{1,p-1}_{\\mathrm{loc}}$, and its weak gradient satisfies a Wolff potential estimate at every Lebesgue point of the weak gradient. Under the additional condition $sp>n$, the solution has a continuous representative that is Fréchet differentiable at every point where the potential is finite. These results give a partial answer to questions raised by Diening and Nowak [Ann. PDE, \\textbf{11}(2025)] and by Diening, Kim, Lee and Nowak~[J. Eur. Math. Soc. (JEMS), 2025] concerning gradient potential estimates for the fractional $p$-Laplacian. The proof combines homogeneous affine decay with constants independent of the affine slope and comparison estimates to obtain an affine excess recurrence. Iteration then yields the Wolff potential bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06924",
  "author_total": 2,
  "authors": [
    {
      "name": "Ying Li"
    },
    {
      "name": "Chao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fzhyw45zhgvt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06924",
  "fulltext_url": null,
  "id": "3fzhyw45zhgvt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06924",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212055636",
  "pdf_url": "https://arxiv.org/pdf/2609.06924",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fzhyw45zhgvt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.06924",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06924"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gradient estimates for the fractional $p$-Laplacian in the superquadratic regime",
  "title_text": "Gradient estimates for the fractional p-Laplacian in the superquadratic regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/3fzhyw45zhgvt",
  "venue": "arXiv",
  "versions": []
}