{
  "abstract": "Zugmeyer~\\cite{Zug} established sharp trace Gagliardo--Nirenberg--Sobolev inequalities on convex cones for $a\\geq n>p>1$. We classify all nonzero real-valued extremals of these inequalities. Let the cone be the epigraph of a finite convex function that is positively homogeneous of degree one, and let $H$ be any norm. We prove that equality holds precisely for functions of the form $A H(x+te+\\ell)^{-(a-p)/(p-1)}$, where $A\\in\\mathbb{R}\\backslash\\{0\\}$, $t>0$, $e=(0,\\ldots,0,1)$, and $\\ell$ belongs to the largest vector subspace contained in the cone. The result includes the critical Sobolev trace inequality at $a=n$, as well as nonsmooth norms and cones, half-spaces, and cones containing lines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28503",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuxuan Zhou"
    },
    {
      "name": "Yingfang Zhang"
    },
    {
      "name": "Wenming Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95r4527q0wt32.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28503",
  "fulltext_url": null,
  "id": "95r4527q0wt32",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28503",
  "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": "W7223082588",
  "pdf_url": "https://arxiv.org/pdf/2610.28503",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95r4527q0wt32.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28503",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28503"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Extremals for Sharp Trace Gagliardo--Nirenberg--Sobolev Inequalities on Convex Cones",
  "title_text": "Extremals for Sharp Trace Gagliardo--Nirenberg--Sobolev Inequalities on Convex Cones",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/95r4527q0wt32",
  "venue": "arXiv",
  "versions": []
}