Peculiar behavior of the principal Laplacian eigenvalue for large negative Robin parameters
| Autor: | Dietze, Charlotte, Pankrashkin, Konstantin |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\Omega\subset\mathbb{R}^n$ with $n\ge 2$ be a bounded Lipschitz domain with outer unit normal $\nu$. For $\alpha\in\mathbb{R}$ let $R_\Omega^\alpha$ be the Laplacian in $\Omega$ with the Robin boundary condition $\partial_\nu u+\alpha u=0$, and denote by $E(R^\alpha_\Omega)$ its principal eigenvalue. In 2017 Bucur, Freitas and Kennedy stated the following open question: Does the limit of the ratio $E(R_\Omega^\alpha)/ \alpha^2$ for $\alpha\to-\infty$ always exist? We give a negative answer. Comment: 19 pages |
| Databáze: | arXiv |
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