Hardy inequalities for large fermionic systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909142060367872 |
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| author | Frank, Rupert L. Hoffmann-Ostenhof, Thomas Laptev, Ari Solovej, Jan Philip |
| author_facet | Frank, Rupert L. Hoffmann-Ostenhof, Thomas Laptev, Ari Solovej, Jan Philip |
| contents | Given $0<s<\frac d2$ with $s\leq 1$, we are interested in the large $N$-behavior of the optimal constant $κ_N$ in the Hardy inequality $\sum_{n=1}^N (-Δ_n)^s \geq κ_N \sum_{n<m} |X_n-X_m|^{-2s}$, when restricted to antisymmetric functions. We show that $N^{1-\frac{2s}d}κ_N$ has a positive, finite limit given by a certain variational problem, thereby generalizing a result of Lieb and Yau related to the Chandrasekhar theory of gravitational collapse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hardy inequalities for large fermionic systems Frank, Rupert L. Hoffmann-Ostenhof, Thomas Laptev, Ari Solovej, Jan Philip Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Spectral Theory Given $0<s<\frac d2$ with $s\leq 1$, we are interested in the large $N$-behavior of the optimal constant $κ_N$ in the Hardy inequality $\sum_{n=1}^N (-Δ_n)^s \geq κ_N \sum_{n<m} |X_n-X_m|^{-2s}$, when restricted to antisymmetric functions. We show that $N^{1-\frac{2s}d}κ_N$ has a positive, finite limit given by a certain variational problem, thereby generalizing a result of Lieb and Yau related to the Chandrasekhar theory of gravitational collapse. |
| title | Hardy inequalities for large fermionic systems |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Spectral Theory |
| url | https://arxiv.org/abs/2403.12640 |