{
  "abstract": "We study the Faber--Krahn problem for the fractional--logarithmic Laplacian $(-Δ)^{s+\\ln}$, $0<s<1$, with Fourier symbol $|ξ|^{2s}\\ln|ξ|^2$. We prove a small-volume and large-volume dichotomy. For sufficiently small volume, balls minimize the first Dirichlet eigenvalue, with rigidity up to translation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15481",
  "author_total": 3,
  "authors": [
    {
      "name": "Huyuan Chen"
    },
    {
      "name": "Rui Chen"
    },
    {
      "name": "Bobo Hua"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c13vmrd1ch0kp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15481",
  "fulltext_url": null,
  "id": "c13vmrd1ch0kp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15481",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213224067",
  "pdf_url": "https://arxiv.org/pdf/2609.15481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c13vmrd1ch0kp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On Faber-Krahn inequality for Dirichlet Fractional-Logarithmic Laplacian",
  "title_text": "On Faber-Krahn inequality for Dirichlet Fractional-Logarithmic Laplacian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/c13vmrd1ch0kp",
  "venue": "arXiv",
  "versions": []
}