{
  "abstract": "We study a class of weighted fourth-order elliptic problems in \\(\\mathbb{R}^4\\) driven by the biharmonic operator and involving Hardy--Hénon type potentials. The nonlinear term has critical exponential growth in the sense of an Adams-type inequality. The weights \\(|x|^a\\) and \\(|x|^b\\) allow us to incorporate singular, vanishing, and unbounded effects in a unified variational framework. We introduce a suitable weighted function space, establish Sobolev-type embeddings, and prove an Adams-type inequality adapted to this setting. Under appropriate structural assumptions on the nonlinearity, we prove the existence of nontrivial weak solutions. We also obtain regularity properties and derive a Pohozaev identity, which leads to a nonexistence result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38078",
  "author_total": 3,
  "authors": [
    {
      "name": "J. C. de Albuquerque"
    },
    {
      "name": "J. Carvalho"
    },
    {
      "name": "L. M. Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdq9gzvh1bqyq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38078",
  "fulltext_url": null,
  "id": "cdq9gzvh1bqyq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38078",
  "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/2610.38078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdq9gzvh1bqyq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in $\\mathbb{R}^4$",
  "title_text": "Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in ℝ^4",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/cdq9gzvh1bqyq",
  "venue": "arXiv",
  "versions": []
}