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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.02428 |
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| _version_ | 1866910282233675776 |
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| author | Cheng, Haoyu |
| author_facet | Cheng, Haoyu |
| contents | We determine the logarithmic growth exponents of the $L^p$ norms, $1\le p\le\infty$, of $L^2$-normalized Laplace eigenfunctions on the unit disk, for both Dirichlet and Neumann boundary conditions. We also prove sharp uniform $L^p$ upper and lower bounds for every $L^2$-normalized Dirichlet eigenfunction and every non-constant Neumann eigenfunction $u_λ$ on the disk. The proof uses stationary phase estimates and integral estimates for Bessel functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact $L^p$ growth rates of Laplace eigenfunctions on the unit disk Cheng, Haoyu Spectral Theory 35P20 (Primary) 35J05, 33C10, 34B30, 58J50 (Secondary) We determine the logarithmic growth exponents of the $L^p$ norms, $1\le p\le\infty$, of $L^2$-normalized Laplace eigenfunctions on the unit disk, for both Dirichlet and Neumann boundary conditions. We also prove sharp uniform $L^p$ upper and lower bounds for every $L^2$-normalized Dirichlet eigenfunction and every non-constant Neumann eigenfunction $u_λ$ on the disk. The proof uses stationary phase estimates and integral estimates for Bessel functions. |
| title | Exact $L^p$ growth rates of Laplace eigenfunctions on the unit disk |
| topic | Spectral Theory 35P20 (Primary) 35J05, 33C10, 34B30, 58J50 (Secondary) |
| url | https://arxiv.org/abs/2606.02428 |