{
  "abstract": "\\noindent Let \\(\\Om\\subset\\R^2\\) be a smooth bounded simply connected domain. We prove that all positive solutions of \\(-Δu=θue^{u^2}\\), with \\(θ>0\\) and zero Dirichlet boundary data, have Dirichlet energy bounded by a constant depending only on \\(\\Om\\). Consequently, the Trudinger--Moser functional has no nonnegative constrained critical points at sufficiently large prescribed energies. The proof combines a weighted Pohozaev identity obtained after conformal change of variables, concentration analysis of normalized measures, and local radial comparison. The comparison hypotheses are obtained from local integral estimates, without an a priori energy bound. An estimate for the exterior Green potential then excludes sequences of unbounded energy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10086",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongtao Hu"
    },
    {
      "name": "Qiaoran Wu"
    },
    {
      "name": "Wenming Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2z8bpfxnjknx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10086",
  "fulltext_url": null,
  "id": "f2z8bpfxnjknx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10086",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221043663",
  "pdf_url": "https://arxiv.org/pdf/2610.10086",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2z8bpfxnjknx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10086",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10086"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A priori Dirichlet energy bounds for positive Trudinger--Moser critical points on simply connected planar domains",
  "title_text": "A priori Dirichlet energy bounds for positive Trudinger--Moser critical points on simply connected planar domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/f2z8bpfxnjknx",
  "venue": "arXiv",
  "versions": []
}