Mathematical Research Letters

Volume 23 (2016)

Number 3

Sharp lower bounds for Coulomb energy

Pages: 621 – 632



Jacopo Bellazzini (Università di Sassari, Italy)

Marco Ghimenti (Dipartimento di Matematica, Università di Pisa, Italy)

Tohru Ozawa (Department of Applied Physics, Waseda University, Tokyo, Japan)


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


radial symmetry, sharp emebeddings, Coulomb energy, fractional Sobolev spaces

2010 Mathematics Subject Classification

39B62, 46E35

Accepted 7 November 2015

Published 8 July 2016