Abstract:Adopting the powerful methods introduced in \cite{li2021carnotcaratheodory, LZ2025}, we investigate the asymptotic behaviour at infinity for the heat kernel associated with the Grushin operator $\Delta_G = \Delta_x + |x|^2 \Delta_u$ on $ \mathbb{R}_x ^n \times \mathbb{R}_u ^{n'} $ for all $ n , \, n' \ge 1 $. We further establish sharp bounds for its spatial derivatives. As a by-product, precise estimates and small-time asymptotic behaviour for the Grushin heat kernel will be provided, as explicit as one can possibly hope for.
| Comments: | 15 pages |
| Subjects: | Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA) |
| MSC classes: | 58J35, 58J37, 35B40, 35K08, 43A85 |
| Cite as: | arXiv:2605.25622 [math.AP] |
| (or arXiv:2605.25622v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25622 arXiv-issued DOI via DataCite (pending registration) |
From: Yimeng Chen [view email]
[v1]
Mon, 25 May 2026 09:26:32 UTC (23 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。