{
  "abstract": "We consider solutions $u, v:Ω\\rightarrow\\mathbb{R}^{N}$ of the Euler-Lagrange equations associated to the variational integral $\\int_Ωf(\\nabla u)dx$, where $Ω$ is an exterior domain in $\\mathbb{R}^{2}$ e.g., the complement of a disk or a half plane, and the density $f$ is of linear growth. Among other things we show that $u|_{\\partialΩ}=v|_{\\partialΩ}$ together with the boundedness of $u-v$ yields that $u=v$ on the entire domain.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01780",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Bildhauer Martin Fuchs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87z4kfbakspcn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01780",
  "fulltext_url": null,
  "id": "87z4kfbakspcn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01780",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01780",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87z4kfbakspcn.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01780",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01780"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness results for the exterior Dirichlet and Neumann problem in two dimensions for the Euler-Lagrange equations of variational integrals with linear growth",
  "title_text": "Uniqueness results for the exterior Dirichlet and Neumann problem in two dimensions for the Euler-Lagrange equations of variational integrals with linear growth",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:10Z",
  "url": "https://research.draconitic.com/paper/87z4kfbakspcn",
  "venue": "arXiv",
  "versions": []
}