{
  "abstract": "For weak solutions to quasilinear degenerate parabolic equations of $p$-Laplace type, a central obstacle in applying the method of intrinsic scaling to prove their Hölder regularity is the derivation of forward-in-time propagation estimate for the spatial measure of level sets. In this paper, we revisit and overcome this difficulty for an inhomogeneous degenerate parabolic $p$-Laplace equation with bounded nonnegative time-independent forcing term and initial data. Our new proof is built upon the temporal Lipschitz estimate that we establish on any time interval separated from the initial time by a positive amount. The strong regularity gain furnished by this estimate allows us to derive the forward propagation of level-set measures directly, thereby bypassing the energy inequality that served as the starting point of the previous approach. Furthermore, we establish space-time $W^{1,\\infty}_{x,t}$ estimates away from the initial time and construct counterexamples to demonstrate the sharpness of the positive waiting-time condition under merely bounded initial data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01724",
  "author_total": 3,
  "authors": [
    {
      "name": "Xia Hao"
    },
    {
      "name": "Yan Li"
    },
    {
      "name": "Zhiwen Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ac92pt1vdqeyh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01724",
  "fulltext_url": null,
  "id": "ac92pt1vdqeyh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01724",
  "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": "W7216124882",
  "pdf_url": "https://arxiv.org/pdf/2610.01724",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ac92pt1vdqeyh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01724",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01724"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regularity for solutions to inhomogeneous degenerate parabolic $p$-Laplace equations",
  "title_text": "Regularity for solutions to inhomogeneous degenerate parabolic p-Laplace equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/ac92pt1vdqeyh",
  "venue": "arXiv",
  "versions": []
}