Hardy inequalities for large fermionic systems
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Given 0 < s < d/2 with s ≤ 1, we are interested in the large N-behavior of the optimal constant κN in the Hardy inequality ΣNn=1(-Δn)s ≥ κN Σn<m |Xn - Xm|-2s, when restricted to antisymmetric functions. We show that N1-2s/d κN 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.
Original language | English |
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Journal | Journal of Spectral Theory |
Volume | 14 |
Issue number | 2 |
Pages (from-to) | 805-835 |
ISSN | 1664-039X |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:
©2024 European Mathematical Society.
- electrostatic inequalities, fermions, Hardy inequalities, semi-classical limit
Research areas
ID: 396649709