{
  "abstract": "We consider the Dirichlet problem $-Δu=|x|^αu^p$, $u>0$ in $Ω$, $u=0$ on $\\partialΩ$, where $Ω\\subset R^N$, $N\\ge 3$, is a bounded domain containing the origin and $α>0$. We prove that a solution exists for every exponent $1<p<p_α=\\frac{N+2+2α}{N-2}$, in particular in the whole Sobolev-supercritical range $\\frac{N+2}{N-2}\\le p<p_α$, provided $Ω$ is invariant under $O(N-1)\\times O(1)$ and satisfies an angular monotonicity condition. This class contains the balls, the oblate ellipsoids of revolution, lens-shaped domains, and non-convex, non-smooth and non star-shaped domains. The solution is obtained by minimizing the Rayleigh quotient on a suitable closed convex cone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39976",
  "author_total": 2,
  "authors": [
    {
      "name": "Francesca Gladiali"
    },
    {
      "name": "Massimo Grossi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58pfs1h2a1fmh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39976",
  "fulltext_url": null,
  "id": "58pfs1h2a1fmh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39976",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58pfs1h2a1fmh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Hénon equation beyond the critical Sobolev exponent",
  "title_text": "The Hénon equation beyond the critical Sobolev exponent",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/58pfs1h2a1fmh",
  "venue": "arXiv",
  "versions": []
}