{
  "abstract": "We obtain sharp regularity for the anisotropic fractional Laplace equation with a right-hand side belonging to a Morrey space. We derive local $C^{σ+λ-n}-$regularity of solutions when $σ+λ-n\\neq1$, where $σ\\in(0,2)$ is the order of the operator and $λ\\in(n-σ,n)$ is the Morrey decay rate of the right-hand side. In the case $σ+λ-n=1$, we show that solutions are locally in the Zygmund class, and hence are Log-Lipschitz continuous. Explicit examples attest to the sharpness of the conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39947",
  "author_total": 2,
  "authors": [
    {
      "name": "Rafayel Teymurazyan"
    },
    {
      "name": "José Miguel Urbano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apek63sbtgd0m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39947",
  "fulltext_url": null,
  "id": "apek63sbtgd0m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39947",
  "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/2610.39947",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apek63sbtgd0m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39947",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39947"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp regularity for the anisotropic fractional Laplacian with Morrey data",
  "title_text": "Sharp regularity for the anisotropic fractional Laplacian with Morrey data",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/apek63sbtgd0m",
  "venue": "arXiv",
  "versions": []
}