{
  "abstract": "We establish small-energy regularity for stationary weak solutions of the Liouville equation $ -Δu=e^u $ in every dimension. It solves a problem left open in Da Lio [Commun. Partial Differ. Equations, 2008] and posed explicitly again by Da Lio and Hyder in [Commun. Contemp. Math. 2025]. The proof relies on the analysis of concentration phenomena for almost stationary fields with structure constraints.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26026",
  "author_total": 4,
  "authors": [
    {
      "name": "Haotong Fu"
    },
    {
      "name": "Kelei Wang"
    },
    {
      "name": "Wei Wang"
    },
    {
      "name": "Ke Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31pppj7rjpd4c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26026",
  "fulltext_url": null,
  "id": "31pppj7rjpd4c",
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  "landing_url": "https://arxiv.org/abs/2609.26026",
  "language": null,
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  "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": "W7214117070",
  "pdf_url": "https://arxiv.org/pdf/2609.26026",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31pppj7rjpd4c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26026",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26026"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Small-energy regularity for stationary weak solutions of the Liouville equation",
  "title_text": "Small-energy regularity for stationary weak solutions of the Liouville equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/31pppj7rjpd4c",
  "venue": "arXiv",
  "versions": []
}