Minimality of the ball for a model of charged liquid droplets

2019/12/15 by Ekaterina Mukoseeva, Mukoseeva, Ekaterina, Giulia Vescovo +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1912.07092

openalex publication_date 2019/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deduce that charged liquid droplets minimizing Debye-Hückel-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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• Ahlfors-regularity for minimizers of a multiphase optimal design problem
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