Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908558723907584 |
|---|---|
| author | Dietze, Charlotte Pankrashkin, Konstantin |
| author_facet | Dietze, Charlotte Pankrashkin, Konstantin |
| contents | Let $Ω\subset\mathbb{R}^n$ with $n\ge 2$ be a bounded Lipschitz domain with outer unit normal $ν$. For $α\in\mathbb{R}$ let $R_Ω^α$ be the Laplacian in $Ω$ with the Robin boundary condition $\partial_νu+αu=0$, and denote by $E(R^α_Ω)$ its principal eigenvalue. In 2017 Bucur, Freitas and Kennedy stated the following open question: Does the limit of the ratio $E(R_Ω^α)/ α^2$ for $α\to-\infty$ always exist? We give a negative answer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters Dietze, Charlotte Pankrashkin, Konstantin Spectral Theory Analysis of PDEs Primary 35P15, Secondary 49R05, 35J05 Let $Ω\subset\mathbb{R}^n$ with $n\ge 2$ be a bounded Lipschitz domain with outer unit normal $ν$. For $α\in\mathbb{R}$ let $R_Ω^α$ be the Laplacian in $Ω$ with the Robin boundary condition $\partial_νu+αu=0$, and denote by $E(R^α_Ω)$ its principal eigenvalue. In 2017 Bucur, Freitas and Kennedy stated the following open question: Does the limit of the ratio $E(R_Ω^α)/ α^2$ for $α\to-\infty$ always exist? We give a negative answer. |
| title | Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters |
| topic | Spectral Theory Analysis of PDEs Primary 35P15, Secondary 49R05, 35J05 |
| url | https://arxiv.org/abs/2412.04061 |