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We prove 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. 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.
@article{AIHPC_2023__40_2_457_0,
author = {Mukoseeva, Ekaterina and Vescovo, Giulia},
title = {Minimality of the ball for a model of charged liquid droplets},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {457--509},
volume = {40},
number = {2},
year = {2023},
doi = {10.4171/aihpc/49},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/49/}
}
TY - JOUR AU - Mukoseeva, Ekaterina AU - Vescovo, Giulia TI - Minimality of the ball for a model of charged liquid droplets JO - Annales de l'I.H.P. Analyse non linéaire PY - 2023 SP - 457 EP - 509 VL - 40 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/49/ DO - 10.4171/aihpc/49 LA - en ID - AIHPC_2023__40_2_457_0 ER -
%0 Journal Article %A Mukoseeva, Ekaterina %A Vescovo, Giulia %T Minimality of the ball for a model of charged liquid droplets %J Annales de l'I.H.P. Analyse non linéaire %D 2023 %P 457-509 %V 40 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/49/ %R 10.4171/aihpc/49 %G en %F AIHPC_2023__40_2_457_0
Mukoseeva, Ekaterina; Vescovo, Giulia. Minimality of the ball for a model of charged liquid droplets. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 2, pp. 457-509. doi: 10.4171/aihpc/49
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