{
  "abstract": "We prove a scale-invariant boundary Harnack inequality and Hölder continuity up to the boundary of quotients of positive fractional $p$-harmonic functions in Reifenberg flat domains with sufficiently small flatness constant, for $0<s<1$ and $2\\le p<2/(1-s)$. The solutions are globally nonnegative, vanish on a common exterior boundary patch, and belong to the natural local energy and $(p-1)$-tail class. Their distant exterior values may be unrelated and unbounded. After normalization at a corkscrew point, the comparison and Hölder constants depend only on $n,s,p$. We first establish local half-space boundary comparison for every $p\\ge2$ and prove relative approximation by the half-space profile in Reifenberg domains. The compactness argument identifies escaped exterior mass and excludes its constant source term. Interior $C^{1,α}$ regularity then yields gradient non-degeneracy and lower increment bounds in a cone of directions. To treat the degenerate kernels produced by linearization, we develop estimates for weighted non-local forms and prove a localized Harnack inequality for bounded quotients, retaining the full exterior interactions. Ordered variational deformations and a common fractional $p$-harmonic majorant yield comparison for solutions with unrelated exterior data. Truncation of distant data and fractional $p$-harmonic replacement extend the estimates from the variational energy class to the natural tail class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21689",
  "author_total": 1,
  "authors": [
    {
      "name": "Kaj Nyström"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zh9wevdb9qf2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21689",
  "fulltext_url": null,
  "id": "1zh9wevdb9qf2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21689",
  "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": "W7222576204",
  "pdf_url": "https://arxiv.org/pdf/2610.21689",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zh9wevdb9qf2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21689",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21689"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundary Harnack inequalities for the fractional $p$-Laplacian in Reifenberg flat domains",
  "title_text": "Boundary Harnack inequalities for the fractional p-Laplacian in Reifenberg flat domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1zh9wevdb9qf2",
  "venue": "arXiv",
  "versions": []
}