{
  "abstract": "We prove that continuous $2$-convex solutions of the $σ_{2}$ equation with a density bounded above and below by positive constants belong to $W^{2,1}_{\\mathrm{loc}}$ in every dimension. If, in addition, the density is continuous, the solutions belong to $W^{2,p}_{\\mathrm{loc}}$ for every $1<p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08297",
  "author_total": 1,
  "authors": [
    {
      "name": "Yasheng Lyu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22y0e4y1vfqer.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08297",
  "fulltext_url": null,
  "id": "22y0e4y1vfqer",
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  "landing_url": "https://arxiv.org/abs/2609.08297",
  "language": null,
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  "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|Geometric Analysis and Curvature Flows"
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  ],
  "openalex": "W7212071055",
  "pdf_url": "https://arxiv.org/pdf/2609.08297",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22y0e4y1vfqer.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08297",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08297"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interior $W^{2,p}$ regularity for the sigma-$2$ equation",
  "title_text": "Interior W^2,p regularity for the sigma-$2$ equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/22y0e4y1vfqer",
  "venue": "arXiv",
  "versions": []
}