{
  "abstract": "In his 1957 paper on the Dirichlet problem for higher-order elliptic equations in the plane, Agmon conjectured that there should exist higher-order equations in dimensions greater than two for which a potential-theoretic approach based on multi-layer integral operators can be successfully implemented. We show that this is indeed the case for the polyharmonic operator $Δ^m$ of arbitrary order $m\\in\\mathbb{N}$ in $\\mathbb{R}^n$, $n\\geq 2$, even in geometrically rough domains permitting singularities beyond the scope of the existing theory of higher-order elliptic boundary value problems. Central to our approach is a new genre of multi-layer singular integral operators, which play for $Δ^m$ the role assumed by the classical harmonic double layer potential in the treatment of the Dirichlet problem for harmonic functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25401",
  "author_total": 4,
  "authors": [
    {
      "name": "Artur Andrade"
    },
    {
      "name": "Dorina Mitrea"
    },
    {
      "name": "Irina Mitrea"
    },
    {
      "name": "Marius Mitrea"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/en4hxae64bsyg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25401",
  "fulltext_url": null,
  "id": "en4hxae64bsyg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25401",
  "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|Differential Equations and Boundary Problems"
    ]
  ],
  "openalex": "W7214094833",
  "pdf_url": "https://arxiv.org/pdf/2609.25401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/en4hxae64bsyg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25401"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Solution to Agmon's Conjecture for the polylaplacian",
  "title_text": "The Solution to Agmon's Conjecture for the polylaplacian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/en4hxae64bsyg",
  "venue": "arXiv",
  "versions": []
}