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We deduce that charged liquid droplets minimizing Debye-H\"uckel-type freeenergy are spherical in the small charge regime. The variational model wasproposed by Muratov and Novaga in 2016 to avoid the ill-posedness of theclassical one. By combining a recent (partial) regularity result with SelectionPrinciple of Cicalese and Leonardi, we prove that the ball is the uniqueminimizer in the small charge regime.

Minimality of the ball for a model of charged liquid droplets