{
  "abstract": "We prove a rigidity result for the problem $Δ_p u=-2$ defined on a ring-shaped domain in $\\mathbb{R}^2$, when homogeneous Dirichlet boundary conditions are imposed and $p\\in(1,2)$. This problem admits a natural physical interpretation, as it describes the steady laminar flow of a generalised Newtonian fluid exhibiting shear-thinning behaviour. Our symmetry result is obtained assuming that the set of maximum points, denoted by $Σ$, is a smooth closed curve, and there are no other critical points outside it; moreover, an appropriate asymptotic expansion of the solution near $Σ$ is required. Although our approach is inspired by the comparison strategy of [arXiv:2505.04458], the main ingredients used there are intrinsically linear and have no direct counterparts for the $p$-Laplacian. This requires the introduction of new ideas and techniques.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20861",
  "author_total": 2,
  "authors": [
    {
      "name": "Virginia Agostiniani"
    },
    {
      "name": "Chiara Bernardini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wsy75eg3a2p2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20861",
  "fulltext_url": null,
  "id": "9wsy75eg3a2p2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20861",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222746380",
  "pdf_url": "https://arxiv.org/pdf/2610.20861",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wsy75eg3a2p2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.20861",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20861"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$p$-Laplace Serrin problem on planar annuli",
  "title_text": "p-Laplace Serrin problem on planar annuli",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/9wsy75eg3a2p2",
  "venue": "arXiv",
  "versions": []
}