{
  "abstract": "We establish a pointwise lower bound for the heat kernel of the elliptic operator $ Λ=(1+|x|^α)Δ+b|x|^{α-2}x\\cdot\\nabla-|x|^β$, where $d\\geq3$, $α>2$, $β>α-2$, and $b\\in\\mathbb R$. For every $τ>0$, we prove that $$ \\begin{aligned} p(t,x,y) &\\geq C_τe^{λ_0t} \\left(\\frac{1+|y|^α}{1+|x|^α}\\right)^{\\frac{b}{2α}} \\frac{(|x||y|)^{-\\frac{d-1}{2}-\\frac{β-α}{4}}}{1+|y|^α}\\\\ &\\quad\\times\\exp \\left[ -\\int_1^{|x|}\\sqrt{\\frac{s^β}{1+s^α}}\\,\\mathrm ds -\\int_1^{|y|}\\sqrt{\\frac{s^β}{1+s^α}}\\,\\mathrm ds \\right] \\end{aligned} $$ for all $t\\geqτ$ and $|x|,|y|\\geq1$, where $λ_0<0$ is the largest eigenvalue of $Λ$ and $C_τ>0$ is independent of $t,x,y$. The proof applies the classical Davies - Simon argument in a weighted symmetric setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29258",
  "author_total": 1,
  "authors": [
    {
      "name": "Sallah Eddine Boutiah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agxbkczfb5gd6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29258",
  "fulltext_url": null,
  "id": "agxbkczfb5gd6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29258",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214375657",
  "pdf_url": "https://arxiv.org/pdf/2609.29258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agxbkczfb5gd6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Lower bounds for heat kernels of elliptic operators with unbounded diffusion, drift, and potential terms",
  "title_text": "Lower bounds for heat kernels of elliptic operators with unbounded diffusion, drift, and potential terms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/agxbkczfb5gd6",
  "venue": "arXiv",
  "versions": []
}