{
  "abstract": "We study vector-valued local minimizers of double phase functionals with two modulating coefficients and logarithmic-type growth. The energy density is $a(x)|Du|^p+b(x)|Du|^p\\log(e+|Du|)$, where the nonnegative coefficients $a(\\cdot)$ and $b(\\cdot)$ may vanish but their sum is bounded away from zero. Assuming that $a(\\cdot)$ is uniformly continuous and that $b(\\cdot)$ satisfies a vanishing log-Hölder continuity condition, we prove that minimizers are locally Hölder continuous for every exponent in $(0,1)$. If both coefficients are Hölder continuous, then the gradient of a minimizer is locally Hölder continuous. The proof combines Gehring-type higher integrability with a comparison argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33479",
  "author_total": 2,
  "authors": [
    {
      "name": "Yumi Kim"
    },
    {
      "name": "Jehan Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ajkb0bb4dbrpf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33479",
  "fulltext_url": null,
  "id": "ajkb0bb4dbrpf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33479",
  "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": "W7214796448",
  "pdf_url": "https://arxiv.org/pdf/2609.33479",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ajkb0bb4dbrpf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33479",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33479"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth",
  "title_text": "Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/ajkb0bb4dbrpf",
  "venue": "arXiv",
  "versions": []
}