{
  "abstract": "We consider weak solutions $u \\in W^{1,n}(U,\\mathbf{R}^{n+1})$ of the $H$-system $- \\operatorname{div} ( |\\mathrm{D} u|^{n-2} \\mathrm{D} u ) = (H \\circ u) \\, \\mathbf{J} u$, where $n \\ge 2$, $U$ is the open unit ball in $\\mathbf{R}^n$, and $H$ is bounded. We show that $u$ is locally bounded if its distortion $|\\mathrm{D} u|^n / |\\mathbf{J} u|$ is bounded on the set where $|u|$ is large. By a result of Fusco, Kristensen, Leone, and Verde, it follows that $u$ is locally Hölder continuous if $H$ is continuous, and continuously differentiable with locally Hölder continuous derivative if $H$ is locally Lipschitz. The proof pushes forward $|\\mathrm{D} u|^{n-2} \\mathrm{D} u \\circ \\mathrm{D} u^*$ by $u$ to a linear functional on continuous compactly supported maps of $\\mathbf{R}^{n+1}$ into $\\operatorname{Hom}(\\mathbf{R}^{n+1},\\mathbf{R}^{n+1})$, whose values on derivatives are controlled by the equation. When the distortion is bounded, this functional satisfies the hypotheses of an inequality of Michael-Simon type for measures satisfying a first-order partial differential equation, due to De Philippis, Gennaioli, Pigati,and Rindler. The inequality yields lower bounds for the mass ratios of the push-forward of $|\\mathrm{D} u|^n \\mathscr{L}^n$ by $u$, and these imply boundedness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06441",
  "author_total": 1,
  "authors": [
    {
      "name": "Sławomir Kolasiński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/de20q0zg314nf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06441",
  "fulltext_url": null,
  "id": "de20q0zg314nf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06441",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220653402",
  "pdf_url": "https://arxiv.org/pdf/2610.06441",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/de20q0zg314nf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.06441",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06441"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regularity for $H$-systems of bounded distortion",
  "title_text": "Regularity for H-systems of bounded distortion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/de20q0zg314nf",
  "venue": "arXiv",
  "versions": []
}