{
  "abstract": "Let $Ω$ be an open bounded connected subset of $\\mathbb{R}^N$, $N \\geq 2$, of class $C^{2,α}$, for $α\\in (0,1)$. Let $p \\geq 2$ and $β>0$. We prove the symmetry of the solution of the $p$-torsion problem with Robin boundary condition subject to the natural overdetermined condition coming from a shape derivative argument and to an extra condition on $β$ and on the minimum of the principal curvatures of $\\partialΩ$. The proof is based on some new integral identities, involving the linearized operator of the $p$-Laplacian applied to the standard $P$-function. In passing we prove some other rigidity results in the spirit of Serrin's and Alexandrov's Theorems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29393",
  "author_total": 2,
  "authors": [
    {
      "name": "Luca Barbato"
    },
    {
      "name": "Riccardo Molinarolo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yd1tfmzn6453.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29393",
  "fulltext_url": null,
  "id": "3yd1tfmzn6453",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29393",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7214322140",
  "pdf_url": "https://arxiv.org/pdf/2609.29393",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3yd1tfmzn6453.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29393",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29393"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Serrin-type overdetermined problem for the $p$-Laplacian with Robin boundary conditions",
  "title_text": "Serrin-type overdetermined problem for the p-Laplacian with Robin boundary conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/3yd1tfmzn6453",
  "venue": "arXiv",
  "versions": []
}