article

Title: Isoperimetric problem with a coulomb repulsive term

Authors: Vesa Julin

Issue: Volume 63 (2014), Issue 1, 77-89

Abstract:

$We consider a non-local isoperimetric problem with a repulsive Coulomb term. In dimension three, this corresponds to Gamow's famous liquid drop model. We show that, whenever the mass is small, the ball is the unique minimizer of the problem, and thus give a partial answer to a conjecture by Choksi and Peletier. The proof is based on a strong version of a quantitative isoperimetric inequality introduced in [N.\ Fusco and V.\ Julin, \textit{A strong form of the quantitative isoperimetric inequality} (2011), preprint].$