Calculus of Variations and Geometric Measure Theory

M. Goldman - B. Ruffini

Equilibrium shapes of charged liquid droplets and related problems: (mostly) a review

created by ruffini on 14 Sep 2017
modified on 24 Mar 2021


Published Paper

Inserted: 14 sep 2017
Last Updated: 24 mar 2021

Journal: Geometric flows
Year: 2017


We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations in the functional. The original contribution of this note is twofold. First, we prove existence of an optimal distribution of charge for a conducting drop subject to an external electric eld. Second, we prove that there exists no optimal conducting drop in this setting.