{
  "abstract": "We consider the Brezis--Nirenberg problem $-Δu = |u|^{2^{*}-2}u + \\varepsilon u$ in a smooth bounded domain $Ω\\subset \\mathbb{R}^{N}$, $N \\geq 5$, with Dirichlet boundary conditions, where $\\varepsilon > 0$ is small. Two multi-peak configurations found in dimension four in \\cite{PRV2} persist. In an annulus, for every even $k \\geq 2$, we construct solutions blowing up at the vertices of a regular $k$-gon with alternating signs. In the ball, we construct solutions blowing up positively at the vertices of a regular $k$-gon in a coordinate plane and negatively at those of a regular $k$-gon in an orthogonal plane, for $2 \\leq k \\leq 5$ if $N = 5,6$ and $2 \\leq k \\leq 4$ if $N \\geq 7$. This range is sharp: for larger $k$ no such solution exists with parameters in a compact set, while otherwise the reduced energy has a unique, non-degenerate critical point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26180",
  "author_total": 1,
  "authors": [
    {
      "name": "Giuseppe Mario Rago"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h9ttz137abnf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26180",
  "fulltext_url": null,
  "id": "4h9ttz137abnf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26180",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.26180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h9ttz137abnf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26180"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sign-changing bubbling solutions on polygons for the Brezis-Nirenberg problem in high dimensions",
  "title_text": "Sign-changing bubbling solutions on polygons for the Brezis-Nirenberg problem in high dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4h9ttz137abnf",
  "venue": "arXiv",
  "versions": []
}