Uniform heat kernel asymptotics for the Grushin operator
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918521276989440 |
|---|---|
| author | Chen, Yimeng Li, Hong-Quan Tang, Jun-Cheng Yang, Jia-Yu |
| author_facet | Chen, Yimeng Li, Hong-Quan Tang, Jun-Cheng Yang, Jia-Yu |
| contents | 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 $Δ_G = Δ_x + |x|^2 Δ_u$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25622 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform heat kernel asymptotics for the Grushin operator Chen, Yimeng Li, Hong-Quan Tang, Jun-Cheng Yang, Jia-Yu Analysis of PDEs Classical Analysis and ODEs 58J35, 58J37, 35B40, 35K08, 43A85 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 $Δ_G = Δ_x + |x|^2 Δ_u$ 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. |
| title | Uniform heat kernel asymptotics for the Grushin operator |
| topic | Analysis of PDEs Classical Analysis and ODEs 58J35, 58J37, 35B40, 35K08, 43A85 |
| url | https://arxiv.org/abs/2605.25622 |