{
  "abstract": "We investigate fractional analogs of Korn's inequality on bounded Lipschitz domains in several contexts. Constrained and unconstrained inequalities are established; constraints include quotient spaces and spaces incorporating various classes of boundary conditions or volume constraints. We also expand the parameters of integrability for which the inequalities hold. Specifically, a fractional Korn's first unconstrained inequality holds for vector fields in the fractional Sobolev space $W^{s,p}(Ω;\\mathbb{R}^n)$ for all $p \\in [1,\\infty]$ and all $s \\in (0,1)$. In the cases $p = 1$ and $p = \\infty$, the inequality has no local analog. We quantify this by investigating the consistency of the inequalities as the differentiability parameter $s \\to 1$; the universal constant in the inequality remains stable for $p \\in (1,\\infty)$ but degenerates for $p \\in \\{1,\\infty\\}$. We introduce an explicit $L^p$-bounded projection operator onto infinitesimal rigid motions as a key tool to quantitatively strengthen the inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33325",
  "author_total": 2,
  "authors": [
    {
      "name": "Tadele Mengesha"
    },
    {
      "name": "James M. Scott"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06t5gqsn63c6c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33325",
  "fulltext_url": null,
  "id": "06t5gqsn63c6c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33325",
  "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": "W7223908035",
  "pdf_url": "https://arxiv.org/pdf/2610.33325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06t5gqsn63c6c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Consistency in fractional Korn's inequalities on Lipschitz domains",
  "title_text": "Consistency in fractional Korn's inequalities on Lipschitz domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/06t5gqsn63c6c",
  "venue": "arXiv",
  "versions": []
}