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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14286 |
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| _version_ | 1866917344497893376 |
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| author | Chen, Bin Deng, Yinbin Guo, Yujin Wang, Chenyang |
| author_facet | Chen, Bin Deng, Yinbin Guo, Yujin Wang, Chenyang |
| contents | We consider ground states of a pseudo-relativistic Fermi system in the $L^2$-critical case. We prove that the system admits ground states, if and only if the attractive strength $a$ satisfies $0<a<D_{4/3,2}$, where $D_{4/3,2}\in(0, \infty)$ is the optimal constant of a dual fractional Lieb--Thirring inequality. The limiting behavior of ground states for the system is further analyzed as $a\nearrow D_{4/3,2}$. As a byproduct, the qualitative properties of optimizers for the dual fractional Lieb-Thirring inequality are also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14286 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Limiting Behavior of $L^2$-Critical Pseudo-Relativistic Fermi Systems Chen, Bin Deng, Yinbin Guo, Yujin Wang, Chenyang Analysis of PDEs We consider ground states of a pseudo-relativistic Fermi system in the $L^2$-critical case. We prove that the system admits ground states, if and only if the attractive strength $a$ satisfies $0<a<D_{4/3,2}$, where $D_{4/3,2}\in(0, \infty)$ is the optimal constant of a dual fractional Lieb--Thirring inequality. The limiting behavior of ground states for the system is further analyzed as $a\nearrow D_{4/3,2}$. As a byproduct, the qualitative properties of optimizers for the dual fractional Lieb-Thirring inequality are also investigated. |
| title | On the Limiting Behavior of $L^2$-Critical Pseudo-Relativistic Fermi Systems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.14286 |