{
  "abstract": "We construct, for any exponent $p\\in(1,\\infty)$, $p$-homogeneous rank-one convex integrands $F\\colon \\mathbb{R}^{2\\times m}\\to \\mathbb{R}$ that are nowhere quasiconvex when $m$ is large. When $p$ is sufficiently close to $4$, such examples can be constructed on $\\mathbb{R}^{2\\times 3}$: for $p=4$, our example is an explicit quartic polynomial. Related constructions give, for every $p$, conjugation- and transposition-invariant examples on $\\mathbb{R}^{d\\times d}$, and examples on $\\mathbb{R}^{4\\times 2}$ for every $p\\neq 2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.03488",
  "author_total": 1,
  "authors": [
    {
      "name": "Gabriele Cassese"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fq378838d6aap.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.03488",
  "fulltext_url": null,
  "id": "fq378838d6aap",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.03488",
  "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": "W7172491280",
  "pdf_url": "https://arxiv.org/pdf/2608.03488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fq378838d6aap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.03488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.03488"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A solution to Morrey's problem in $\\mathbb{R}^{2\\times m}$",
  "title_text": "A solution to Morrey's problem in ℝ^2× m",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/fq378838d6aap",
  "venue": "arXiv",
  "versions": []
}