{
  "abstract": "We study the homogenization of an elliptic eigenvalue problem in a periodically perforated domain, where the spectral parameter appears both in the equation, through a bulk density $q$, and in a Steklov condition on the boundaries of the holes, through a surface density $ρ$, and where the resulting bulk--surface spectral measure $q\\,dy+ρ\\,dS_y$ is indefinite. We show that the asymptotic behavior of the spectrum depends essentially on whether the combined mean $m_{\\rm eff}=\\int_{Y^*}q\\,dy+\\int_Γρ\\,dS_y$ is positive, negative, or zero. In all three cases, we prove convergence of eigenvalue clusters with multiplicity and of eigenspaces and, under additional regularity, $O(\\varepsilon)$ estimates for the shifted or rescaled eigenvalues, spectral projectors, and aligned eigenspaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05487",
  "author_total": 1,
  "authors": [
    {
      "name": "Hermann DOUANLA"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgkmahk6rc2tj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05487",
  "fulltext_url": null,
  "id": "cgkmahk6rc2tj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05487",
  "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",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7220697494",
  "pdf_url": "https://arxiv.org/pdf/2610.05487",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgkmahk6rc2tj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05487",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05487"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains",
  "title_text": "Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/cgkmahk6rc2tj",
  "venue": "arXiv",
  "versions": []
}