Hardy inequalities for large fermionic systems
Rupert L. Frank
Ludwig-Maximilians Universität München, München, Germany; Munich Center for Quantum Science and Technology, München, Germany; Caltech, Pasadena, USAThomas Hoffmann-Ostenhof
University of Vienna, Wien, AustriaAri Laptev
Imperial College London, London, UK; Sirius University of Science and Technology, Sochi, RussiaJan Philip Solovej
University of Copenhagen, Copenhagen, Denmark
![Hardy inequalities for large fermionic systems cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-14-issue-2.png&w=3840&q=90)
Abstract
Given with , we are interested in the large -behavior of the optimal constant in the Hardy inequality , when restricted to antisymmetric functions. We show that 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.
Cite this article
Rupert L. Frank, Thomas Hoffmann-Ostenhof, Ari Laptev, Jan Philip Solovej, Hardy inequalities for large fermionic systems. J. Spectr. Theory 14 (2024), no. 2, pp. 805–835
DOI 10.4171/JST/511