{
  "abstract": "This paper establishes interior $H^{s,p}$ regularity for weak solutions to fractional nonlocal equations in divergence form with general kernels. Under the $(δ, R)$-vanishing condition on the coefficients, we prove that for $p>2$, if the source term $f\\in L^p_{loc}$, then the solution $u\\in H^{s,p}_{loc}$. In contrast to Byun and Kim \\cite{BK2025}, our result holds in the borderline case for $f$ without requiring differentiability assumptions. Our approach simplifies previous methods by using the stability properties of the fractional gradient to derive the good-inequality directly, thereby avoiding reliance on maximal functions. The proof integrates Vitali's covering lemma, Hardy-Littlewood maximal theory, self-improving estimates, and compactness arguments. This work extends classical $W^{1,p}$ regularity to fractional nonlocal settings under minimal kernel assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07606",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhenjie Li"
    },
    {
      "name": "Lihe Wang"
    },
    {
      "name": "Chunqin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fybmhq49tcr0p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07606",
  "fulltext_url": null,
  "id": "fybmhq49tcr0p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07606",
  "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/2611.07606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fybmhq49tcr0p.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07606"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "H^{s,p} estimates for weak solutions of fractional nonlocal equations in divergence form",
  "title_text": "H^{s,p} estimates for weak solutions of fractional nonlocal equations in divergence form",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/fybmhq49tcr0p",
  "venue": "arXiv",
  "versions": []
}