First mixed Laplace eigenfunctions with no hot spots
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929365062778880 |
|---|---|
| author | Hatcher, Lawford |
| author_facet | Hatcher, Lawford |
| contents | The hot spots conjecture of J. Rauch states that the second Neumann eigenfunction of the Laplace operator on a bounded Lipschitz domain in $\mathbb{R}^n$ attains its extrema only on the boundary of the domain. We present an analogous problem for domains with mixed Dirichlet-Neumann boundary conditions. We then solve this problem for Euclidean triangles and a class of planar domains bounded by the graphs of certain piecewise smooth functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | First mixed Laplace eigenfunctions with no hot spots Hatcher, Lawford Analysis of PDEs 35P05, 35B38, 35J05, 35J25, 58J50 The hot spots conjecture of J. Rauch states that the second Neumann eigenfunction of the Laplace operator on a bounded Lipschitz domain in $\mathbb{R}^n$ attains its extrema only on the boundary of the domain. We present an analogous problem for domains with mixed Dirichlet-Neumann boundary conditions. We then solve this problem for Euclidean triangles and a class of planar domains bounded by the graphs of certain piecewise smooth functions. |
| title | First mixed Laplace eigenfunctions with no hot spots |
| topic | Analysis of PDEs 35P05, 35B38, 35J05, 35J25, 58J50 |
| url | https://arxiv.org/abs/2401.01514 |