{
  "abstract": "We study positive weak singular solutions of the subcritical fractional Hartree equation \\[ (-Δ)^s u = \\left( \\int_{\\mathbb{R}^N\\setminusΓ} \\frac{u^p(y)}{|x-y|^μ}d y \\right)u^q \\quad\\text{in }\\mathbb{R}^N\\setminusΓ, \\] where \\(0<s<1\\), \\(N>2s\\), \\(0<μ<N\\), and \\(Γ\\subset\\{x_1=0\\}\\) is compact with zero \\((s,2)\\)-capacity. For solutions with a nonremovable singular point on $Γ$, we prove hyperplane symmetry and strict transverse monotonicity under global Lebesgue integrability conditions. For $N\\ge2$, we also prove these conclusions under upper bounds on $p$ and $q$, using only the integrability required for weak solutions. We also establish local regularity and construct solutions with logarithmic singularities along a line segment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24684",
  "author_total": 3,
  "authors": [
    {
      "name": "Guangze Gu"
    },
    {
      "name": "Aleks Jevnikar"
    },
    {
      "name": "Zhipeng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5p8xgn6baehbj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24684",
  "fulltext_url": null,
  "id": "5p8xgn6baehbj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24684",
  "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": "W7223029355",
  "pdf_url": "https://arxiv.org/pdf/2610.24684",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5p8xgn6baehbj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24684",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24684"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Symmetry and Monotonicity for Subcritical Fractional Hartree Equations with Singular Sets of Zero Capacity",
  "title_text": "Symmetry and Monotonicity for Subcritical Fractional Hartree Equations with Singular Sets of Zero Capacity",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:45Z",
  "url": "https://research.draconitic.com/paper/5p8xgn6baehbj",
  "venue": "arXiv",
  "versions": []
}