{
  "abstract": "Let $1 \\leq q \\le 2$ and denote by $2 \\leq q'$ its corresponding conjugate exponent. We prove the continuity of solutions $u \\in W^{1,(\\frac{n}{n-1},q')}(B^n, \\mathbb{R}^m)$ to the critical elliptic system $-Δu = Ω\\cdot \\nabla u$ in dimension $n \\ge 3$, where the potential $Ω\\in L^{(n,q)}(B^n, \\mathfrak{so}(m) \\otimes \\wedge^1)$ is antisymmetric. First, we construct $P \\in W^{1,(n,q)}(B^n, \\mathrm{SO}(m))$ such that the PDE can be rewritten as $-\\operatorname{div}(P^{-1}du) = \\ast dξ\\cdot P^{-1}du$, which is nearly a Jacobian structure up to the rotation $P$. Second, we provide a Rivière's $\\mathrm{GL}(m)$-Gauge in order to establish a \"full\" $(A,B)$-conservation law, i.e. $-\\operatorname{div}(Adu)=d^\\ast B \\cdot du$. We show that the assumption on $Ω\\in L^{(n,q)} (B^n, \\mathfrak{so}(m) \\otimes \\wedge^1) $ for $q\\leq 2$ is optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00826",
  "author_total": 1,
  "authors": [
    {
      "name": "Carolin Bayer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3a0q2et7w09da.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00826",
  "fulltext_url": null,
  "id": "3a0q2et7w09da",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00826",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7206184588",
  "pdf_url": "https://arxiv.org/pdf/2609.00826",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3a0q2et7w09da.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.00826",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00826"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Regularity and Rivière's ${GL}(m)$-Gauge Construction for Elliptic Systems with Antisymmetric Potentials in Arbitrary Dimensions",
  "title_text": "Regularity and Rivière's GL(m)-Gauge Construction for Elliptic Systems with Antisymmetric Potentials in Arbitrary Dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/3a0q2et7w09da",
  "venue": "arXiv",
  "versions": []
}