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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.15221 |
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| _version_ | 1866913999499558912 |
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| author | Chen, Xiao-Ping Tang, Chun-Lei |
| author_facet | Chen, Xiao-Ping Tang, Chun-Lei |
| contents | This paper focus on the symmetry and symmetry breaking about the second order Hydrogen Uncertainty Principle. \emph{Firstly}, by choosing a suitable test function, we give a negative answer to the conjecture presented by Cazacu, Flynn and Lam in [\emph{J. Funct. Anal.} \textbf{283} (2022), Paper No. 109659, 37 pp] for $N\in\{2,3\}$, and emphasizing the symmetry breaking phenomenon. \emph{Secondly}, we obtain a family of sharp weighted second order Hydrogen Uncertainty Principle, and prove the extremal functions are radial, which extends the work of Duong and Nguyen [The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle, arXiv:2102.01425]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking Chen, Xiao-Ping Tang, Chun-Lei Analysis of PDEs This paper focus on the symmetry and symmetry breaking about the second order Hydrogen Uncertainty Principle. \emph{Firstly}, by choosing a suitable test function, we give a negative answer to the conjecture presented by Cazacu, Flynn and Lam in [\emph{J. Funct. Anal.} \textbf{283} (2022), Paper No. 109659, 37 pp] for $N\in\{2,3\}$, and emphasizing the symmetry breaking phenomenon. \emph{Secondly}, we obtain a family of sharp weighted second order Hydrogen Uncertainty Principle, and prove the extremal functions are radial, which extends the work of Duong and Nguyen [The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle, arXiv:2102.01425]. |
| title | On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.15221 |