{
  "abstract": "Let $Ω$ be a bounded domain in $R^d$. Denote by $λ_k$ (resp. $μ_k$) the eigenvalues of the Laplace operator in $Ω$ with Dirichlet (resp. Neumann) boundary conditions. Denote by $Ψ= Ψ(d,k,Ω)$ the shift of indices in the inequality $μ_{k+Ψ} \\le λ_k$. We are interested to describe the behaviour of $Ψ$ for large $d$. We prove that a) $Ψ(d,1,Ω) \\ge C (e/2)^d$ for all domains $Ω$; and b) $Ψ(d,k,Ω) \\ge C (e/2)^d$ for all $k$ and all convex domains $Ω$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.30120",
  "author_total": 1,
  "authors": [
    {
      "name": "N. Filonov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/crbf0tg4zdtgr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.30120",
  "fulltext_url": null,
  "id": "crbf0tg4zdtgr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.30120",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7166684619",
  "pdf_url": "https://arxiv.org/pdf/2606.30120",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/crbf0tg4zdtgr.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.30120",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.30120"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Inequalities between Dirichlet and Neumann eigenvalues in large dimensions",
  "title_text": "Inequalities between Dirichlet and Neumann eigenvalues in large dimensions",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/crbf0tg4zdtgr",
  "venue": "arXiv",
  "versions": []
}