{
  "abstract": "Let $D\\subset\\mathbb{R}^n$, $n\\ge2$, be a bounded convex domain, and let $u_D$ be the torsion function for the restricted half-Laplacian. We prove that $D^2u_D$ is negative definite at every point of $D$. The argument is based on the reflected harmonic extension in a slit domain. Quantitative Schauder estimates in slit domains yield parameter-uniform estimates for the first and second derivatives of the edge remainder; a Schur-complement calculation then determines the inertia of the extended Hessian near the slit edge. Superharmonicity of the logarithmic Hessian determinant and the Gleason--Wolff zero-set theorem exclude interior degeneracy. A method of continuity starting from the unit ball proves the result for smooth uniformly convex domains, and an exhaustion argument treats arbitrary bounded convex domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19586",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiahuan Li"
    },
    {
      "name": "Shujun Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aepwx29mgfwcf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19586",
  "fulltext_url": null,
  "id": "aepwx29mgfwcf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19586",
  "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": "W7203887367",
  "pdf_url": "https://arxiv.org/pdf/2608.19586",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aepwx29mgfwcf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2608.19586",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19586"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strict Concavity of the Torsion Function for the Restricted Half-Laplacian in Bounded Convex Domains",
  "title_text": "Strict Concavity of the Torsion Function for the Restricted Half-Laplacian in Bounded Convex Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/aepwx29mgfwcf",
  "venue": "arXiv",
  "versions": []
}