Finite-Rank Optimizers for the mass--supercritical Lieb--Thirring and Hardy--Lieb--Thirring Inequalities
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909873722097664 |
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| author | Duong, Giao Ky Le, Thi Minh Thao Nam, Phan Thành Nguyen, Phuoc-Tai |
| author_facet | Duong, Giao Ky Le, Thi Minh Thao Nam, Phan Thành Nguyen, Phuoc-Tai |
| contents | We establish the existence of finite-rank operators for an interpolation version of the Lieb--Thirring inequality in the mass--supercritical case, thereby extending a result of Hong, Kwon, and Yoon in 2019 to the full parameter regime. Our method also applies to the Hardy--Lieb--Thirring inequality, where the existence of optimizers faces additional difficulties due to the singularity of the inverse-square potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24148 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-Rank Optimizers for the mass--supercritical Lieb--Thirring and Hardy--Lieb--Thirring Inequalities Duong, Giao Ky Le, Thi Minh Thao Nam, Phan Thành Nguyen, Phuoc-Tai Mathematical Physics Functional Analysis Spectral Theory 81Q10, 35P15, 47A10, 81Q10, 47A75, 49J35 We establish the existence of finite-rank operators for an interpolation version of the Lieb--Thirring inequality in the mass--supercritical case, thereby extending a result of Hong, Kwon, and Yoon in 2019 to the full parameter regime. Our method also applies to the Hardy--Lieb--Thirring inequality, where the existence of optimizers faces additional difficulties due to the singularity of the inverse-square potential. |
| title | Finite-Rank Optimizers for the mass--supercritical Lieb--Thirring and Hardy--Lieb--Thirring Inequalities |
| topic | Mathematical Physics Functional Analysis Spectral Theory 81Q10, 35P15, 47A10, 81Q10, 47A75, 49J35 |
| url | https://arxiv.org/abs/2510.24148 |