{
  "abstract": "Let $Ω\\subset\\mathbb{R}^2$ be a smooth bounded domain and let $0<α<2$. We study the exponential Choquard functional \\[ \\mathcal{F}_β(u)=\\int_Ω\\int_Ω \\frac{e^{βu^2(x)}e^{βu^2(y)}}{|x-y|^α}d xd y \\] on the unit Dirichlet ball of $H_0^1(Ω)$. We establish the sharp boundedness threshold $β_*=(4-α)π$ and prove attainment of the critical supremum. More precisely, we determine the exact concentration level at every point of $\\overlineΩ$ in terms of the regular part of the Dirichlet Green function. The concentration upper bound follows from the classical planar Trudinger--Moser concentration formula and the sharp Hardy--Littlewood--Sobolev inequality, after separating the background contribution. A test function obtained by matching a logarithmic profile to the Green function attains this bound asymptotically. Its exact Dirichlet normalization produces a strictly positive lower-order correction, which rules out concentration of maximizing sequences. We also prove the Euler--Lagrange equation, positivity, and regularity of extremals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25313",
  "author_total": 1,
  "authors": [
    {
      "name": "Jinkai Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zg9715s6pese.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25313",
  "fulltext_url": null,
  "id": "8zg9715s6pese",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25313",
  "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": "W7223058829",
  "pdf_url": "https://arxiv.org/pdf/2610.25313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zg9715s6pese.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp concentration levels and extremal functions for a planar Choquard-type Trudinger--Moser inequality",
  "title_text": "Sharp concentration levels and extremal functions for a planar Choquard-type Trudinger--Moser inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/8zg9715s6pese",
  "venue": "arXiv",
  "versions": []
}