{
  "abstract": "We establish sharp estimates for the discrete optimal constant of the fractional Sobolev inequality in dimension $N\\geq 1$, with fractional exponent $s\\in (0,\\min\\{1,N/2\\})$. The convergence rates that we establish take place for the Galerkin approximation with piecewise linear elements, when the problem is posed in the unit ball, for which we employ a quasi-uniform and regular mesh. Since the infimum defining the fractional Sobolev constant is not attained on bounded domains, these estimates quantify how far a piecewise affine mesh of size $h$ can resolve the concentration of the optimizers: the discrete minimizers are close to bubbles concentrated at the scale $h^{2(2-s)/(N+4(1-s))}$, and the energy gap is exactly of order $h^{2(2-s)(N-2s)/(N+4(1-s))}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.13347",
  "author_total": 2,
  "authors": [
    {
      "name": "Andreea Dima"
    },
    {
      "name": "Liviu I. Ignat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ppy5chccfv12.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.13347",
  "fulltext_url": null,
  "id": "3ppy5chccfv12",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.13347",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
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      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7161148225",
  "pdf_url": "https://arxiv.org/pdf/2605.13347",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ppy5chccfv12.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2605.13347",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.13347"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Galerkin Approximation of the Fractional Sobolev Constant",
  "title_text": "Galerkin Approximation of the Fractional Sobolev Constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/3ppy5chccfv12",
  "venue": "arXiv",
  "versions": []
}