{
  "abstract": "We establish a sharp Faber-Krahn inequality for the normalized (or game-theoretic) $p$-Laplacian, proving that, for $p\\geq 2$, the ball uniquely minimizes the principal Dirichlet eigenvalue among bounded connected Lipschitz domains of prescribed volume satisfying a uniform exterior sphere condition. More generally, we prove the same inequality for the family of homogeneous operators $|Du|^γΔ_p^N u$, with $p>1$ and $-1<γ\\le p-2$. Unlike the classical $p$-Laplacian, these operators lack a variational structure, preventing the use of standard symmetrization arguments. Our proof overcomes this difficulty through a level-set approach: it relies on a flux identity for the eigenvalue, for which a variational interpretation re-emerges in the special case where the domain is a ball.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23593",
  "author_total": 2,
  "authors": [
    {
      "name": "Graziano Crasta"
    },
    {
      "name": "Ilaria Fragalà"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4jv4z3enjm51.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23593",
  "fulltext_url": null,
  "id": "f4jv4z3enjm51",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23593",
  "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": "W7222926767",
  "pdf_url": "https://arxiv.org/pdf/2610.23593",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4jv4z3enjm51.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23593",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23593"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Faber--Krahn inequality for homogeneous normalized $p$-Laplacian type operators",
  "title_text": "Faber--Krahn inequality for homogeneous normalized p-Laplacian type operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/f4jv4z3enjm51",
  "venue": "arXiv",
  "versions": []
}