{
  "abstract": "For $2\\le k<n$, we prove pointwise gradient bounds for proper weak $k$-convex functions in terms of a local average and a Wolff potential of the full Hessian measure $F_k[u]$. The estimate yields local Lipschitz regularity for $F_k[u]=f$ with $f\\in L^{n/k,1/k}_{\\mathrm{loc}}$, and for $F_k[u]=|Du|^p$ when $0<p<nk/(n-k)$. Both the Lorentz index $1/k$ and the upper bound on $p$ are sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08184",
  "author_total": 3,
  "authors": [
    {
      "name": "Huajie Liu"
    },
    {
      "name": "Shiguang Ma"
    },
    {
      "name": "Shengyang Zang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2npkcark7b0dy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08184",
  "fulltext_url": null,
  "id": "2npkcark7b0dy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08184",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2npkcark7b0dy.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gradient potential estimates for k-Hessian equations",
  "title_text": "Gradient potential estimates for k-Hessian equations",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/2npkcark7b0dy",
  "venue": "arXiv",
  "versions": []
}