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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.16911 |
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| _version_ | 1866909438320836608 |
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| author | Chen, Xiujin Yang, Xiaoping |
| author_facet | Chen, Xiujin Yang, Xiaoping |
| contents | Let Ω be a bounded domain in R^n with C^{1,1} boundary and let u_λ be a Neumann
Laplace eigenfunction in Ω with eigenvalue λ. We show that the (n - 1)-dimensional
Hausdorff measure of the zero set of u_λ does not exceed C\sqrtλ. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains Chen, Xiujin Yang, Xiaoping Analysis of PDEs 35B05 Let Ω be a bounded domain in R^n with C^{1,1} boundary and let u_λ be a Neumann Laplace eigenfunction in Ω with eigenvalue λ. We show that the (n - 1)-dimensional Hausdorff measure of the zero set of u_λ does not exceed C\sqrtλ. |
| title | The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains |
| topic | Analysis of PDEs 35B05 |
| url | https://arxiv.org/abs/2412.16911 |