{
  "abstract": "We consider entire solutions $u$: $\\mathbb{R}^n \\rightarrow \\mathbb{R}$, $n \\ge 2$, of the equation $\\operatorname{div}(\\nabla f(\\nabla u)) = 0$ with convex density $f$: $\\mathbb{R}^n \\rightarrow \\mathbb{R}$ given for example by $f(\\nabla u) = \\sum_{i=1}^n |\\partial_i u|^{p_i}$ with exponents $p_i \\ge 2$ including Giaquinta's example for the choice $p_1 = \\dots = p_{n-1} = 2$, $p_n = 4$. If $n \\le 2 + \\min\\{p_i\\}$ holds, then we have the Liouville property: the boundedness of $u$ implies its constancy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11369",
  "author_total": 2,
  "authors": [
    {
      "name": "Michael Bildhauer"
    },
    {
      "name": "Martin Fuchs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1txbja6ethp0n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11369",
  "fulltext_url": null,
  "id": "1txbja6ethp0n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11369",
  "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": "W7221132815",
  "pdf_url": "https://arxiv.org/pdf/2610.11369",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1txbja6ethp0n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11369",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11369"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Giaquinta's example revisited: the Liouville property for a class of nonuniformly elliptic equations in low dimensions",
  "title_text": "Giaquinta's example revisited: the Liouville property for a class of nonuniformly elliptic equations in low dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/1txbja6ethp0n",
  "venue": "arXiv",
  "versions": []
}