First mixed Laplace eigenfunctions with no hot spots
| Autor: | Hatcher, Lawford |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Formatted and revised for publication in the Proceedings of the AMS. 15 pages, 3 figures |
| Databáze: | arXiv |
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