{
  "abstract": "We study autonomous elliptic systems with Uhlenbeck structure of the form \\[ -\\operatorname{div}\\big(\\mathfrak a(|Du|)Du\\big)=0 \\quad \\text{in }\\ Ω\\subset \\mathbb R^n \\] Under two-sided quantitative $(p,q)$-growth conditions on $\\mathfrak a$, we prove gradient Hölder continuity with constants and exponent depending only on the dimensions, $p$ and $q$. This improves the classical theory initiated by Uhlenbeck by removing the continuity requirement on $\\mathfrak a'$. The proof uses nonlinear comparison systems whose regularity follows from a scalar uniformly elliptic equation. Under weaker $(p,q)$-growth conditions on the convex function $φ(t):=\\int_0^t s\\mathfrak a(s)\\,ds$, we obtain local $W^{1,s}$-regularity for every $s>1$, and hence Hölder continuity of solutions with every exponent less than one. An additional lower growth condition on $\\mathfrak a$ yields local Lipschitz continuity, even when $\\mathfrak a$ is discontinuous.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08635",
  "author_total": 1,
  "authors": [
    {
      "name": "Jihoon Ok"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czf7drkrpndry.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08635",
  "fulltext_url": null,
  "id": "czf7drkrpndry",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08635",
  "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/2611.08635",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czf7drkrpndry.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08635",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08635"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regularity of elliptic systems with Uhlenbeck structure",
  "title_text": "Regularity of elliptic systems with Uhlenbeck structure",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/czf7drkrpndry",
  "venue": "arXiv",
  "versions": []
}