The Robin heat kernel and its expansion via Robin eigenfunctions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915348640432128 |
|---|---|
| author | Meng, Yifeng Wang, Kui |
| author_facet | Meng, Yifeng Wang, Kui |
| contents | We prove the existence and uniqueness of the Robin heat kernel on compact Riemannian manifolds with smooth boundary for Robin parameter $α\in\mathbb{R}$, expressed as a spectral expansion in terms of Robin eigenvalues and eigenfunctions. For the non-negative parameter regime ($α\ge 0$), we present a direct proof based on trace Sobolev inequalities and eigenfunction estimates. The case of negative parameters ($α<0$) requires novel analytical techniques to handle $L^\infty$ estimates of Robin eigenfunctions, addressing challenges not present in the non-negative case. Our result extends the the classical Dirichlet and Neumann cases to the less-studied negative parameter regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15092 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Robin heat kernel and its expansion via Robin eigenfunctions Meng, Yifeng Wang, Kui Analysis of PDEs 35P15, 53C21 We prove the existence and uniqueness of the Robin heat kernel on compact Riemannian manifolds with smooth boundary for Robin parameter $α\in\mathbb{R}$, expressed as a spectral expansion in terms of Robin eigenvalues and eigenfunctions. For the non-negative parameter regime ($α\ge 0$), we present a direct proof based on trace Sobolev inequalities and eigenfunction estimates. The case of negative parameters ($α<0$) requires novel analytical techniques to handle $L^\infty$ estimates of Robin eigenfunctions, addressing challenges not present in the non-negative case. Our result extends the the classical Dirichlet and Neumann cases to the less-studied negative parameter regime. |
| title | The Robin heat kernel and its expansion via Robin eigenfunctions |
| topic | Analysis of PDEs 35P15, 53C21 |
| url | https://arxiv.org/abs/2505.15092 |