{
  "abstract": "We study bounded viscosity solutions of the degenerate or singular parabolic equation \\[ u_t-|Du|^γΔ_p^{\\mathrm{N}}u=f \\qquad \\text{in } Q_1, \\] where \\[ Δ_p^{\\mathrm{N}}u := Δu+(p-2) \\left\\langle D^2u\\frac{Du}{|Du|}, \\frac{Du}{|Du|} \\right\\rangle, \\qquad -1<γ<\\infty,\\quad 1<p<\\infty, \\] and $f\\in C^0(Q_1)\\cap L^\\infty(Q_1)$. Given any prescribed $α\\in(0,1)$, we prove that there exists $\\varepsilon=\\varepsilon(n,α)>0$ such that \\[ |p-2|+|γ|\\leq\\varepsilon \\quad\\Longrightarrow\\quad u\\in C_{\\mathrm{loc}}^{1+α,\\frac{1+α}{2}}(Q_1). \\] In particular, the spatial gradient Hölder exponent can be chosen arbitrarily close to $ 1 $ as $(p,γ)\\to(2,0)$. This extends the result of Andrade and Santos (Calc. Var. Partial Differential Equations \\textbf{61}, Paper No. 196, 2022) for $γ=0$ to the joint regime $(p,γ)\\to(2,0)$ and answers affirmatively the question raised in Remark~1.1 therein.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34855",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiangwen Wang"
    },
    {
      "name": "Yini Zhang"
    },
    {
      "name": "Feida Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0kx54mvms70ed.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34855",
  "fulltext_url": null,
  "id": "0kx54mvms70ed",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34855",
  "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": "W7214774322",
  "pdf_url": "https://arxiv.org/pdf/2609.34855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0kx54mvms70ed.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations",
  "title_text": "Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/0kx54mvms70ed",
  "venue": "arXiv",
  "versions": []
}