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arXiv · 2605.25622

Uniform heat kernel asymptotics for the Grushin operator

Yimeng Chen·Hong-Quan Li·Jun-Cheng Tang·Jia-Yu Yang
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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.

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Yimeng Chen, Hong-Quan Li, Jun-Cheng Tang, Jia-Yu Yang. 2026-05-25. Uniform heat kernel asymptotics for the Grushin operator. https://arxiv.org/abs/2605.25622

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