{
  "abstract": "For $m\\geq 2$, we give a complete characterisation of the continuous functions on $\\mathbb{R}^m$ that are divergences of continuously differentiable vector fields. The characterisation is formulated in terms of distributions and, equivalently, in terms of the continuous dual of a suitably topologised subspace of the Arens--Eells space. The two implications yield contrasting applications. First, there exists a compactly supported continuous function which is the divergence of a bounded Lipschitz vector field but not of any continuously differentiable vector field. Second, every continuous function whose distributional partial derivatives are locally $m$-integrable (the critical exponent for Sobolev embedding) is the divergence of a continuously differentiable vector field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35452",
  "author_total": 1,
  "authors": [
    {
      "name": "Thierry De Pauw"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7p11twc2a27vf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35452",
  "fulltext_url": null,
  "id": "7p11twc2a27vf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35452",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Mathematical and Theoretical Analysis"
    ]
  ],
  "openalex": "W7223780582",
  "pdf_url": "https://arxiv.org/pdf/2610.35452",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7p11twc2a27vf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35452",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35452"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The divergence of continuously differentiable vector fields",
  "title_text": "The divergence of continuously differentiable vector fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/7p11twc2a27vf",
  "venue": "arXiv",
  "versions": []
}