{
  "abstract": "We establish boundary Harnack inequalities for non-negative solutions of the Kolmogorov equation \\[ \\mathcal Ku=Δ_xu+x\\cdot\\nabla_yu-\\partial_tu=0 \\] in non-characteristic intrinsic Lipschitz graph domains whose defining functions may depend on the higher-order variable \\(y_m\\). Earlier theory required independence of \\(y_m\\). We replace this symmetry by quantitative asymptotic cylindricality, measured by a scale-invariant \\(C^{0,1/3}_{y_m}\\) defect. The perturbative comparison theorem applies whenever this defect is sufficiently small, and hence at all sufficiently small scales for \\(C^{0,α}_{y_m}\\) graphs with \\(α>1/3\\), as well as under a vanishing critical cylindrical modulus. We obtain local comparability and intrinsic Hölder continuity of quotients of positive solutions, together with a Hölder estimate for their logarithmic quotient. The proof combines local boundary estimates, valid without \\(y_m\\)-independence, with a global rigidity argument for cylindrical blow-up limits. The central issue is uniform balance of forward and backward reference values. If this balance fails at collapsing scales, maximal-scale selection and a second rescaling produce a non-negative polynomial-growth Dirichlet solution in an unbounded cylindrical domain that vanishes at the backward reference point but not at the forward one. We exclude this configuration using boundary-energy and mean-value estimates, finite-dimensionality of spaces of polynomial-growth solutions, and translation invariance in \\(y_m\\). The resulting finite-dimensional translation representation yields real-analytic dependence on \\(y_m\\). Propagation of zeros, analytic continuation along invariant fibres, and a Tikhonov uniqueness argument then force the limiting solution to vanish identically. The exponent \\(1/3\\) is critical because \\(y_m\\) has homogeneous degree three.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29813",
  "author_total": 1,
  "authors": [
    {
      "name": "Kaj Nyström"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8k1v9y6ta2nds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29813",
  "fulltext_url": null,
  "id": "8k1v9y6ta2nds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29813",
  "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": "W7204966774",
  "pdf_url": "https://arxiv.org/pdf/2608.29813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8k1v9y6ta2nds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Boundary Harnack inequalities for Kolmogorov equations in asymptotically cylindrical Lipschitz domains",
  "title_text": "Boundary Harnack inequalities for Kolmogorov equations in asymptotically cylindrical Lipschitz domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/8k1v9y6ta2nds",
  "venue": "arXiv",
  "versions": []
}