{
  "abstract": "In this paper, we consider second order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatial $A_2$-weight. We prove that having a generalized fundamental solution with upper Gaussian bounds is equivalent to Moser’s $L^2$-$L^\\infty$ estimates for local weak solutions. In the special case of real coefficients, Moser's $L^2$-$L^\\infty$ estimates are known, which provide an easier proof of Gaussian upper bounds, and a known Harnack inequality is then used to derive Gaussian lower bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2503.07569",
  "author_total": 1,
  "authors": [
    {
      "name": "Khalid Baadi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvcbp70f9z85f.bib",
  "cited_by": 0,
  "doi": "10.1007/s00028-026-01201-1",
  "fulltext_url": null,
  "id": "fvcbp70f9z85f",
  "issns": [
    "1424-3199",
    "1424-3202"
  ],
  "landing_url": "https://cnrs.hal.science/hal-04985360v4",
  "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": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-ca"
    ],
    [
      "hal",
      "1.math.math-fa"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W4415016172",
  "pdf_url": "https://cnrs.hal.science/hal-04985360/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": "Springer Verlag",
  "ris": "https://research.draconitic.com/paper/fvcbp70f9z85f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-04985360",
      "source": "hal",
      "url": "https://cnrs.hal.science/hal-04985360v4"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds",
  "title_text": "Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:50Z",
  "url": "https://research.draconitic.com/paper/fvcbp70f9z85f",
  "venue": "Journal of Evolution Equations",
  "versions": []
}