{
  "abstract": "The $W^{1,p}$ estimate for uniformly elliptic operators of divergence form with VMO coefficients is classical. In particular, this provides $W^{1,p}$ estimates for elliptic operators with coefficients in $W^{1,n}$. However, this theory does not yield constants in the estimates controlled by the $W^{1,n}$ norm of the coefficients, since the total $W^{1,n}$ norm does not control the rate of decay for the mean oscillation. In this work, we establish uniform estimates for divergence-form elliptic systems whose coefficients lie in the critical Sobolev--Lorentz spaces $W^{1,(n,s)}$ with $1\\le s<\\infty$, have an $L^\\infty$-bounded spatially symmetric part, and satisfy an integral ellipticity condition. The constant in the estimate is controlled by the corresponding norms of coefficients and the ellipticity constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22366",
  "author_total": 1,
  "authors": [
    {
      "name": "Tian Lan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ysyk805wqa47.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22366",
  "fulltext_url": null,
  "id": "1ysyk805wqa47",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22366",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.22366",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ysyk805wqa47.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22366",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22366"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniform estimates for elliptic systems with critical Sobolev coefficients",
  "title_text": "Uniform estimates for elliptic systems with critical Sobolev coefficients",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/1ysyk805wqa47",
  "venue": "arXiv",
  "versions": []
}