{
  "abstract": "We prove that, on a bounded uniformly convex domain of class $C^{3,1}$, the first Robin eigenfunction is strictly log-concave and the Robin torsion function is strictly $1/2$-concave for all sufficiently large Robin parameters. This means that Conjecture 1.1 of Andrews, Clutterbuck and Hauer holds for uniformly convex $C^{3,1}$ domains in any dimension, and settles an open problem posed by Crasta and Fragalà when the domain has $C^{3,1}$ regularity. Our proof derives suitable uniform $C^2$-decay estimates by maximum principle arguments, thereby removing the imposed higher-order boundary regularity assumption required previously.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06223",
  "author_total": 2,
  "authors": [
    {
      "name": "Dong Ye"
    },
    {
      "name": "Dekai Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8qwep8bz4df1g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06223",
  "fulltext_url": null,
  "id": "8qwep8bz4df1g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06223",
  "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": "W7212032392",
  "pdf_url": "https://arxiv.org/pdf/2609.06223",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8qwep8bz4df1g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06223",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06223"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Concavity Properties of Robin Solutions on $C^{3,1}$ Uniformly Convex Domains",
  "title_text": "Concavity Properties of Robin Solutions on C^3,1 Uniformly Convex Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/8qwep8bz4df1g",
  "venue": "arXiv",
  "versions": []
}