We prove that charged liquid droplets minimizing Debye-Huckel-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. Combining a recent (partial) regularity result with the selection principle of Cicalese and Leonardi, we prove that the ball is the unique minimizer in the small charge regime.
Minimality of the ball for a model of charged liquid droplets / Mukoseeva, Ekaterina; Vescovo, Giulia. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 40:2(2022), pp. 457-509. [10.4171/aihpc/49]
Minimality of the ball for a model of charged liquid droplets
Mukoseeva, Ekaterina;Vescovo, Giulia
2022-01-01
Abstract
We prove that charged liquid droplets minimizing Debye-Huckel-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. Combining a recent (partial) regularity result with the selection principle of Cicalese and Leonardi, we prove that the ball is the unique minimizer in the small charge regime.| File | Dimensione | Formato | |
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