{
  "abstract": "In this article, we establish the interior gradient estimates for $k$-Hessian equations with measure data. We use the ideas from the potential theories for the $p$-Laplacian type equations and pointwise estimates of $k$-subharmonic functions by Labutin. The interior gradient regularity is optimal for $k\\geqslant3$, while for $k=2$, we prove the interior $W^{2,1+\\varepsilon}$ and $C^{1,α}$ estimates for $2$-subharmonic solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38846",
  "author_total": 1,
  "authors": [
    {
      "name": "Rongxun He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nd7rrvhsaxc0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38846",
  "fulltext_url": null,
  "id": "3nd7rrvhsaxc0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38846",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38846",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nd7rrvhsaxc0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38846",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38846"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gradient Estimates for Hessian Equations with Measure Data",
  "title_text": "Gradient Estimates for Hessian Equations with Measure Data",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3nd7rrvhsaxc0",
  "venue": "arXiv",
  "versions": []
}