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arXiv · 1912.07092

Minimality of the ball for a model of charged liquid droplets

Ekaterina Mukoseeva·Giulia Vescovo
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Abstract

We deduce that charged liquid droplets minimizing Debye-H\"uckel-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.

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Ekaterina Mukoseeva, Giulia Vescovo. 2019-12-15. Minimality of the ball for a model of charged liquid droplets. https://arxiv.org/abs/1912.07092

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