{
  "abstract": "We prove a Faber-Krahn inequality for the first eigenvalue of the $p$-Hermite operator (the weighted $p$-Laplacian with Gaussian weight) on Lipschitz domains in $\\R^n$ under Robin boundary conditions with positive Robin parameter. The main result states that, among all domains of given Gaussian measure, the first eigenvalue is minimized by a half-space, and equality holds only for half-spaces. This extends the classical Faber-Krahn inequalities for the $p$-Laplacian \\cite{BucurCV} to the $p$-Hermite operator and generalizes the linear case \\cite{ChiacchioMathann} to the full nonlinear regime $p>1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01269",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaomei Sun"
    },
    {
      "name": "Kui Wang"
    },
    {
      "name": "Anqiang Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0843p2jcq4h44.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01269",
  "fulltext_url": null,
  "id": "0843p2jcq4h44",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01269",
  "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.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.01269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0843p2jcq4h44.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01269"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Faber-Krahn inequality for $p$-Hermite operators",
  "title_text": "The Faber-Krahn inequality for p-Hermite operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/0843p2jcq4h44",
  "venue": "arXiv",
  "versions": []
}