{
  "abstract": "The existence of minimizer for stability of the fractional Sobolev inequality and the stability of Beckner conformal Log-Sobolev inequality (the endpoint case of fractional Sobolev inequality) have been established by König and Chen-Lu-Tang. The existence of minimizer for stability of the Log-Sobolev inequality is unsolved. In this paper, we solve this problem. For every $n\\geq2$, we prove that the sharp $L^2$-stability constant of Beckner conformal log-Sobolev inequality on $\\mathbb S^n$ is attained and is strictly less than $\\frac{2\\log2}{n}$. Moreover, the normalized stability constant of the fractional Sobolev inequality converges to the stability constant of the log-Sobolev inequality as $s\\to0^+$. After Hersch normalization, every sequence of $L^{p_{s_k}}$-normalized minimizers for stability of the fractional Sobolev inequality, with $s_k\\to0^+$, has a subsequence converging strongly in $L^2(\\mathbb S^n)$ to an $L^2$-normalized minimizer of stability of the log-Sobolev inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18327",
  "author_total": 2,
  "authors": [
    {
      "name": "Lu Chen"
    },
    {
      "name": "Bohan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7cjzjbxtb5njv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18327",
  "fulltext_url": null,
  "id": "7cjzjbxtb5njv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18327",
  "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": "W7221790719",
  "pdf_url": "https://arxiv.org/pdf/2610.18327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7cjzjbxtb5njv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Attainment of the sharp stability constant of Beckner conformal log-Sobolev inequality",
  "title_text": "Attainment of the sharp stability constant of Beckner conformal log-Sobolev inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/7cjzjbxtb5njv",
  "venue": "arXiv",
  "versions": []
}