{
  "abstract": "In this paper, we consider the local minimizers to a class of non-autonomous functional with double-phase Orlicz growth: \\begin{equation*} u \\in W^{1,1}(Ω; \\mathbb{R}^N) \\mapsto \\int_Ω\\Big( {φ_1}\\big(|Du|_{\\mathbb{A}^u}\\big) + a(x)\\,{φ_2} \\big(|Du|_{\\mathbb{A}^u}\\big) \\Big)\\, dx, \\end{equation*} where $|Du|_{\\mathbb{A}^u} := \\big\\langle \\mathbb{A}(x,u)\\,Du, Du \\big\\rangle^{\\frac{1}{2}}$ with $\\mathbb{A}(x,u) = \\big\\{A^{αβ}_{ij}(x, u)\\big\\}_{i,j = 1\\cdots N}^{α,β= 1\\cdots n}$ as the uniformly elliptic bounded symmetric tensor field, and $φ_k(\\cdot)$ for $k=1,2$ are two different $N$-functions. We prove the partial regularity of their local minimizers if the continuity modulus of $a(\\cdot)$ and $φ_k(\\cdot)$ are fit for the gap conditions, and $\\mathbb{A}(x,u)$ meets an optimal regularity in $(x,u)$. This is an extension from the single Orlicz growth functional to the double-phase one based on an essential improvement of several important inequalities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31242",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenrui Chang"
    },
    {
      "name": "Shenzhou Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9k27sjph1dz48.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31242",
  "fulltext_url": null,
  "id": "9k27sjph1dz48",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31242",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.31242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9k27sjph1dz48.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Partial regularity for local minimizers of functionals with double-phase Orlicz growth",
  "title_text": "Partial regularity for local minimizers of functionals with double-phase Orlicz growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/9k27sjph1dz48",
  "venue": "arXiv",
  "versions": []
}