{
  "abstract": "This paper investigates intrinsic critical Sobolev-curl constants on bounded domains and the structure of finite-energy solutions to the critical curl-curl equation in R^3. First, for 1< p < 3, we prove that the intrinsic critical p-curl constant on (0, a)\\times D is bounded above by a^{p/3} times a Sobolev quotient on D. The proof uses an aligned test field whose optimal curl-free correction vanishes. Consequently, these constants tend to zero along thin convex boxes. For p = 2, we construct explicit convex and nonconvex domains with intrinsic constant below the sharp scalar Sobolev constant. The nonconvex example gives an affirmative answer to the domain-existence question in Problem 5 of Mederski and Szulkin(Arch. Ration. Mech. Anal. 241 (2021), 1815-1842), while the convex example disproves the lower bound stated there for convex domains. Concerning their Problem 2, we obtain an implicit Newtonian representation of finite-energy solutions and exclude two special forms of solutions. These structural results do not yet provide an explicit ground state or an unconditional ground-state decay rate as asked in Problem 2.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14529",
  "author_total": 4,
  "authors": [
    {
      "name": "Yong Liu"
    },
    {
      "name": "Jun Wang"
    },
    {
      "name": "Xuan Wang"
    },
    {
      "name": "Wen Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1azb6bevpw4hc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14529",
  "fulltext_url": null,
  "id": "1azb6bevpw4hc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14529",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221798625",
  "pdf_url": "https://arxiv.org/pdf/2610.14529",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1azb6bevpw4hc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14529",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14529"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Domain dependence of Sobolev-curl constants and structure of critical curl-curl solutions",
  "title_text": "Domain dependence of Sobolev-curl constants and structure of critical curl-curl solutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1azb6bevpw4hc",
  "venue": "arXiv",
  "versions": []
}