{
  "abstract": "We develop a boundary value and potential theory for elliptic operators \\[ L=-\\Div(A\\nabla)+\\B\\cdot\\nabla \\] with form-bounded drift in one-sided chord-arc domains. Assuming that the positive part of $\\Div\\B$ has sufficiently small form bound, we establish local regularity estimates and solvability of the Dirichlet problem, and construct the associated harmonic measure. Under the additional assumption $\\Div\\B\\le0$, we construct a Green's function and prove pointwise and gradient estimates. For the characteristic distributional identity with a Dirac mass at the pole to hold, we will additionally assume either $\\Div\\B=0$ or $\\B\\in L^{n,1}_{\\textup{loc}}(Ω)$. Moreover, in the divergence-free case, we obtain a local lower bound for the Green's function, CFMS estimates, doubling of harmonic measure, a comparison principle for nonnegative solutions with zero trace, and a change of pole formula. Finally, using AI, we construct, in the upper half-space, an operator of the form $-Δ+\\B\\cdot\\nabla$ with $\\B$ form-bounded and divergence-free, whose harmonic measure exhibits dimension drop.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19983",
  "author_total": 2,
  "authors": [
    {
      "name": "Svitlana Mayboroda"
    },
    {
      "name": "Alberto Pacati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ajwhpah6ch51w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19983",
  "fulltext_url": null,
  "id": "ajwhpah6ch51w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19983",
  "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|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7222186712",
  "pdf_url": "https://arxiv.org/pdf/2610.19983",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ajwhpah6ch51w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.19983",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19983"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Elliptic theory and dimension drop for operators with divergence-free form-bounded drifts in one-sided chord-arc domains",
  "title_text": "Elliptic theory and dimension drop for operators with divergence-free form-bounded drifts in one-sided chord-arc domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/ajwhpah6ch51w",
  "venue": "arXiv",
  "versions": []
}