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

Michael Goldman (1) , Berardo Ruffini (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 IMAG - Institut Montpelliérain Alexander Grothendieck

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 field. Second, we prove that there exists no optimal conducting drop in this setting.

Domaines: Equations aux dérivées partielles [math.AP]

Michael Goldman, Berardo Ruffini. Equilibrium shapes of charged droplets and related problems: (mostly) a review. Geometric Flows, 2017, 2, pp.94-104. ⟨10.1515/geofl-2017-0004⟩. ⟨hal-01587341⟩