The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities
@article{Frank2021TheNS, title={The Nonlinear Schr{\"o}dinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities}, author={Rupert L. Frank and David Gontier and Mathieu Lewin}, journal={Communications in Mathematical Physics}, year={2021}, volume={384}, pages={17831828} }
In this paper we disprove part of 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 Schrödinger operator $$\Delta +V(x)$$

Δ
+
V
(
x
)
are raised to the power $$\kappa $$
κ
is never given by the onebound state case when $$\kappa >\max (0,2d/2)$$
κ
>
max
(
0
,
2

d
/
2
)
in space dimension $$d\ge 1$$
d
≥
1
. When in addition $$\kappa \ge…
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