Hausdorff measure bounds for nodal sets of Steklov eigenfunctions
| Autor: | Decio, Stefano |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Analysis & PDE 17 (2024) 1237-1259 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/apde.2024.17.1237 |
| Popis: | We study nodal sets of Steklov eigenfunctions in a bounded domain with $\mathcal{C}^2$ boundary. Our first result is a lower bound for the Hausdorff measure of the nodal set: we show that for $u_{\lambda}$ a Steklov eigenfunction, with eigenvalue $\lambda\neq 0$, $\mathcal{H}^{d-1}(\{u_{\lambda}=0\})\geq c_{\Omega}$, where $c_{\Omega}$ is independent of $\lambda$. We also prove an almost sharp upper bound, namely $\mathcal{H}^{d-1}(\{u_{\lambda}=0\})\leq C_{\Omega}\lambda\log(\lambda+e)$. Comment: 28 pages, minor revisions. Version accepted for publication in Analysis & PDE |
| Databáze: | arXiv |
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