Calculus of Variations and Geometric Measure Theory

E. Mukoseeva - G. Vescovo

Minimality of the ball for a model of charged liquid droplets

created by mukoseeva on 16 Dec 2019
modified on 25 Nov 2020


Submitted Paper

Inserted: 16 dec 2019
Last Updated: 25 nov 2020

Year: 2019


We deduce that charged liquid droplets minimizing Debye-Huckel-type free energy are spherical in the small charge regime. The variational model was proposed by Muratov and Novaga in 2016 to avoid the ill-posedness of the classical one. By combining a recent (partial) regularity result with Selection Principle of Cicalese and Leonardi, we prove that the ball is the unique minimizer in the small charge regime.