{
  "abstract": "We study vector-valued local minimizers of the borderline double phase functional whose integrand is $|D\\mathbf{w}|^p+a(x)|D\\mathbf{w}|^p\\log^γ(e+|D\\mathbf{w}|)$, where $p>1$, $γ>0$ and the coefficient $a(\\cdot)$ is nonnegative and bounded. If the modulus of continuity $ω(\\cdot)$ of $a(\\cdot)$ satisfies $ω(r)\\log^γ(1/r)\\to0$ as $r\\to0$, then minimizers are locally Hölder continuous for every exponent less than one. If $a(\\cdot)$ is Hölder continuous, then the gradients of minimizers are locally Hölder continuous. In the vector-valued setting these results were previously available only for $γ=1$. The proof combines a comparison with frozen functionals, whose regularity theory applies uniformly in the frozen coefficient, with the higher integrability of minimizers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16900",
  "author_total": 2,
  "authors": [
    {
      "name": "Youlin Choi"
    },
    {
      "name": "Jehan Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fpfax5nhcp41e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16900",
  "fulltext_url": null,
  "id": "fpfax5nhcp41e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16900",
  "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|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221824033",
  "pdf_url": "https://arxiv.org/pdf/2610.16900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fpfax5nhcp41e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Borderline double phase functionals with powers of the logarithm: regularity in the vectorial case",
  "title_text": "Borderline double phase functionals with powers of the logarithm: regularity in the vectorial case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/fpfax5nhcp41e",
  "venue": "arXiv",
  "versions": []
}