Hausdorff measure bound for the nodal sets of Neumann Laplace eigenfunctions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909129223700480 |
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| author | Fazliani, Shaghayegh |
| author_facet | Fazliani, Shaghayegh |
| contents | We study the nodal sets of Neumann Laplace eigenfunctions in a bounded domain with $\mathcal{C}^{1,1}$ boundary. We show that for $u_λ$ such that $Δu_λ+ λu_λ= 0 $ with the Neumann boundary condition $\partial_νu_λ= 0$, we have $\mathcal{H}^{n-1}(\{u_λ= 0\}) \leq C \sqrtλ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09686 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hausdorff measure bound for the nodal sets of Neumann Laplace eigenfunctions Fazliani, Shaghayegh Analysis of PDEs Differential Geometry Spectral Theory 35P30, 42B37 We study the nodal sets of Neumann Laplace eigenfunctions in a bounded domain with $\mathcal{C}^{1,1}$ boundary. We show that for $u_λ$ such that $Δu_λ+ λu_λ= 0 $ with the Neumann boundary condition $\partial_νu_λ= 0$, we have $\mathcal{H}^{n-1}(\{u_λ= 0\}) \leq C \sqrtλ$. |
| title | Hausdorff measure bound for the nodal sets of Neumann Laplace eigenfunctions |
| topic | Analysis of PDEs Differential Geometry Spectral Theory 35P30, 42B37 |
| url | https://arxiv.org/abs/2311.09686 |