4 problems

The Schrödinger operator $H=-\Delta+V$ on $\mathbb{R}^{d}$ has negative eigenvalues $\lambda_n(-\Delta+V)$, and the Lieb–Thirring inequality is … Here $V_-(x)=\max\{0,-V(x)\}$, and…

Let $K_d$ be the optimal constant in the kinetic-energy inequality referred to as equation (kinetic), and let $K_d^{\mathrm{one}}$ and $K_d^{\mathrm{cl}}$ be the corresponding one-…

Let $L_{\gamma,1}$ be the optimal Lieb–Thirring constant in dimension $1$, and let $L_{\gamma,1}^{\mathrm{cl}}$ denote the semiclassical constant. Lieb–Thirring conjecture in dimen…

Let $s>0$, $d\geq 1$, and $\lambda>0$. For the Lieb–Thirring inequality with kinetic energy $(-\Delta)^s$ and repulsive interaction $\lambda\lvert x_i-x_j\rvert^{-2s}$, let…