{
  "abstract": "This paper is concerned with the existence and local gradient regularity of solutions to a quasilinear elliptic Dirichlet problem with finite Radon measure and a degenerate matrix-valued weight. Under a small log-BMO condition on $\\mathbb M$, we first prove the existence of a SOLA (solution obtained by a limit of approximations) and then establish a local Calderón-Zygmund estimate for $|\\mathbb{M}|^{\\frac{1}{p-1}}\\mathbb{M} Du$ in terms of the fractional maximal function $\\mathcal{M}_1(μ)^{\\frac{1}{p-1}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09594",
  "author_total": 3,
  "authors": [
    {
      "name": "Sun-Sig Byun"
    },
    {
      "name": "Xiatong Li"
    },
    {
      "name": "Yeonghun Youn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vwvb2xpvfqh8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09594",
  "fulltext_url": null,
  "id": "2vwvb2xpvfqh8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09594",
  "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": "W7221056046",
  "pdf_url": "https://arxiv.org/pdf/2610.09594",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vwvb2xpvfqh8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09594",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09594"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regularity Estimates for Quasilinear Elliptic Equations with Measure Data and Matrix-Valued Weight",
  "title_text": "Regularity Estimates for Quasilinear Elliptic Equations with Measure Data and Matrix-Valued Weight",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/2vwvb2xpvfqh8",
  "venue": "arXiv",
  "versions": []
}