荷电液滴的平衡形状及相关问题：（主要）综述
Equilibrium shapes of charged droplets and related problems: (mostly) a review
摘要：
本文综述了近年来有关荷电液滴平衡形状的一些结果。我们证明了自然变分模型是不适定的，以及如何通过限制竞争对手类或在泛函中添加惩罚来克服这一点。本说明的原始贡献是双重的。首先，我们证明了存在一个最佳分布的电荷进行外电场的导电滴。其次，我们证明了在这种情况下，不存在最佳的传导下降。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
