Sharp lower bounds for Coulomb energy

Abstract

We prove $L^p$ lower bounds for Coulomb energy for radially symmetric functions in ${\dot{H}}^s({\mathbb{R}}^3)$ with $\frac{1}{2}<s<\frac{3}{2}$. In case $\frac{1}{2}<s\le 1$ we show that the lower bounds are sharp.

10 pages; proof of Theorem 0.4 has been simplified and a simple error fixed

References in corpus (1)

• Ground states for semi-relativistic Schrödinger-Poisson-Slater energies