{
  "abstract": "In this work, we consider relative overdetermined problems for the first eigenfunction of the Laplacian for domains in cones, and the related question of minimizing the first eigenvalue among sets of a given fixed measure. By means of a shape derivative analysis, we show that the spherical sector is a critical shape and obtain a geometric condition on the cone for its stability/instability. By a concentration-compactness argument, we prove the existence of a minimizer, which moreover is bounded, open, connected, and whose relative boundary is regular almost everywhere. By another domain variation argument, we conclude that the minimizers admit a solution for the overdetermined problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12879",
  "author_total": 1,
  "authors": [
    {
      "name": "Danilo Gregorin Afonso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1360yrn4zdakk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12879",
  "fulltext_url": null,
  "id": "1360yrn4zdakk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12879",
  "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"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213072734",
  "pdf_url": "https://arxiv.org/pdf/2609.12879",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1360yrn4zdakk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12879",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12879"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Non-radial minimizers for the first eigenvalue of the Laplacian in cones and a related overdetermined problem",
  "title_text": "Non-radial minimizers for the first eigenvalue of the Laplacian in cones and a related overdetermined problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/1360yrn4zdakk",
  "venue": "arXiv",
  "versions": []
}