Finite-Rank Optimizers for the mass--supercritical Lieb--Thirring and Hardy--Lieb--Thirring Inequalities

Abstract

We establish the existence of finite-rank operators for an interpolation version of the Lieb--Thirring inequality in the mass--supercritical case, thereby extending a result of Hong, Kwon, and Yoon in 2019 to the full parameter regime. Our method also applies to the Hardy--Lieb--Thirring inequality, where the existence of optimizers faces additional difficulties due to the singularity of the inverse-square potential.