{
  "abstract": "We investigate critical polyharmonic equations of the type: $$ Lu = |u|^{2^\\sharp-2} u \\quad \\text{ in } Ω$$ with Dirichlet boundary conditions, in a smooth bounded domain $Ω$ of $\\mathbb{R}^n$. Here $L$ is an elliptic differential operator of integer order $2 \\le 2k < n$ whose leading order term is $(-Δ)^k$ and $2^\\sharp = \\frac{2n}{n-2k}$ is the critical Sobolev exponent. Our main result establishes, in large dimensions, uniform \\emph{a priori} bounds in $C^{2k}(\\overlineΩ)$ for bounded-energy solutions of this problem, that only depend on an upper bound on the energy. We prove this under a coercivity assumption of sorts on the lower-order terms of $L$. Our results are sharp, at least when $k=1$. Our approach uses asymptotic analysis techniques and in the course of the proof we obtain in particular a new global pointwise description of bounded-energy blowing-up solutions for this problem, which is of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.29690",
  "author_total": 2,
  "authors": [
    {
      "name": "Lorenzo Carletti"
    },
    {
      "name": "Bruno Premoselli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvkjn8rryxf5p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.29690",
  "fulltext_url": null,
  "id": "cvkjn8rryxf5p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.29690",
  "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": "W7162769552",
  "pdf_url": "https://arxiv.org/pdf/2605.29690",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvkjn8rryxf5p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2605.29690",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.29690"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A priori bounds for energy-bounded solutions of critical polyharmonic equations",
  "title_text": "A priori bounds for energy-bounded solutions of critical polyharmonic equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/cvkjn8rryxf5p",
  "venue": "arXiv",
  "versions": []
}