{
  "abstract": "In this paper, we establish a Brezis-Merle type inequality for very weak solutions of the biharmonic Dirichlet problem in the four-dimensional unit ball. By combining this inequality with moving-plane arguments, we obtain uniform a priori estimates for positive solutions of semilinear biharmonic equations with exponential nonlinearities in both the subcritical and critical regimes. As an application of these estimates, we prove the existence of a positive solution by means of topological methods. We also extend the analysis to a class of non-variational cooperative systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27212",
  "author_total": 3,
  "authors": [
    {
      "name": "João Marcos do Ó"
    },
    {
      "name": "Federica Sani"
    },
    {
      "name": "Victor Rafael Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6v5g0t0csbcf4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27212",
  "fulltext_url": null,
  "id": "6v5g0t0csbcf4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27212",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223112583",
  "pdf_url": "https://arxiv.org/pdf/2610.27212",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6v5g0t0csbcf4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27212",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27212"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Brezis--Merle inequality for the biharmonic operator with Dirichlet boundary conditions in four-dimensional balls",
  "title_text": "A Brezis--Merle inequality for the biharmonic operator with Dirichlet boundary conditions in four-dimensional balls",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/6v5g0t0csbcf4",
  "venue": "arXiv",
  "versions": []
}