{
  "abstract": "We prove local Calderón-Zygmund estimates for distributional solutions to non-uniformly elliptic equations in divergence form modeled on the energy density $a(x)G(|z|)+b(x)H(|z|)$, where $G$ and $H$ are Young functions and $a(\\cdot)$, $b(\\cdot)$ are nonnegative coefficients, Hölder continuous with exponents $α$ and $β$. Either coefficient may vanish, and only their sum is bounded away from zero, so that each phase can dominate or disappear. Under a gap condition that reduces to $q/p\\le1+\\min\\{α,β\\}/n$ for $G(t)=t^p$ and $H(t)=t^q$, including the borderline case of equality, we show that the energy density of the gradient inherits the Orlicz integrability of the energy density of the datum. The proof combines a fractional differentiability estimate, which gives higher integrability up to the borderline growth, with comparison arguments that freeze the two coefficients in the appropriate order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26543",
  "author_total": 2,
  "authors": [
    {
      "name": "Jehan Oh"
    },
    {
      "name": "Ambesh Kumar Pandey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dykgkgp5t5eg3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26543",
  "fulltext_url": null,
  "id": "dykgkgp5t5eg3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26543",
  "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": "W7204525153",
  "pdf_url": "https://arxiv.org/pdf/2608.26543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dykgkgp5t5eg3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.26543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gradient estimates for generalized double phase problems with two modulating coefficients",
  "title_text": "Gradient estimates for generalized double phase problems with two modulating coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dykgkgp5t5eg3",
  "venue": "arXiv",
  "versions": []
}