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 10 electric field. Second, we prove that there exists no optimal conducting drop in this setting.
Equilibrium shapes of charged liquid droplets and related problems: (mostly) a review.
Ruffini B
2017
Abstract
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 10 electric field. Second, we prove that there exists no optimal conducting drop in this setting.File in questo prodotto:
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