{
  "abstract": "We consider the following degenerate parabolic equation on a bounded domain of $\\mathbb{R}^d$ containing $0$: $\\partial_t u - \\nabla\\cdot(\\varphi(t, x) \\nabla u)= 0 $, where $\\varphi$ is a rough weight behaving like $|x|^\\theta$ near $0$ for some $\\theta \\geq 2$, and $u$ satisfies Neumann boundary condition. We prove that this equation admits a heat kernel with upper and lower Gaussian-type bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29325",
  "author_total": 1,
  "authors": [
    {
      "name": "Hector Bouton"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aa1fygf9fjwfw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29325",
  "fulltext_url": null,
  "id": "aa1fygf9fjwfw",
  "issns": [],
  "landing_url": "https://hal.science/hal-05800356v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223190120",
  "pdf_url": "https://hal.science/hal-05800356/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aa1fygf9fjwfw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:57Z",
      "native_id": "hal-05800356",
      "source": "hal",
      "url": "https://hal.science/hal-05800356v1"
    },
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Upper and lower bounds for heat kernels with very strong degeneracy",
  "title_text": "Upper and lower bounds for heat kernels with very strong degeneracy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/aa1fygf9fjwfw",
  "venue": "HAL",
  "versions": []
}