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Corpus ID: 211083038

The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities

@article{Frank2020TheNS,
title={The nonlinear Schr{\"o}dinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities},
author={R. Frank and D. Gontier and M. Lewin},
journal={arXiv: Analysis of PDEs},
year={2020}
}

In this paper we disprove a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb-Thirring constant when the eigenvalues of a Schrodinger operator −Δ+V(x) are raised to the power κ is never given by the one-bound state case when κ > max(0,2−d/2) in space dimension d ≥ 1. When in addition κ ≥ 1 we prove that this best constant is never attained for a potential having finitely many eigenvalues. The method to obtain the first result… CONTINUE READING