Sharp lower bounds for Coulomb energy

TL;DR

This paper establishes sharp lower bounds for Coulomb energy in radially symmetric functions within certain Sobolev spaces, providing precise estimates that are optimal in specific cases.

Contribution

It introduces new sharp lower bounds for Coulomb energy in radially symmetric Sobolev spaces, extending understanding of energy estimates in mathematical physics.

Findings

Established $L^p$ lower bounds for Coulomb energy

Proved sharpness of bounds for $\frac{1}{2}<s\leq1$

Extended bounds to functions in $\dot H^s(\mathbb{R}^3)$

Abstract

We prove $L^p$ lower bounds for Coulomb energy for radially symmetric functions in $\dot H^s(\R^3)$ with $\frac 12 <s<\frac{3}{2}$. In case $\frac 12 <s \leq 1$ we show that the lower bounds are sharp.