# Sharp Lieb-Thirring inequalities in high dimensions

@article{Laptev1999SharpLI,
title={Sharp Lieb-Thirring inequalities in high dimensions},
author={Ari Laptev and Timo Weidl},
journal={Acta Mathematica},
year={1999},
volume={184},
pages={87-111}
}
• Published 3 March 1999
• Mathematics
• Acta Mathematica
We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge 1$. (revised, to appear in Acta Math)
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