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Article Dans Une Revue Analysis & PDE Année : 2018

On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint

Résumé

We study a variational problem modeling the behavior at equilibrium of charged liquid drops under convexity constraint. After proving well-posedness of the model, we show C 1,1-regularity of minimizers for the Coulombic interaction in dimension two. As a by-product we obtain that balls are the unique minimizers for small charge. Eventually, we study the asymptotic behavior of minimizers, as the charge goes to infinity.
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Dates et versions

hal-01281469 , version 1 (02-03-2016)
hal-01281469 , version 2 (13-09-2017)
hal-01281469 , version 3 (20-06-2018)

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Michael Goldman, Matteo Novaga, Berardo Ruffini. On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint. Analysis & PDE, 2018, 11 (5), pp.1113-1142. ⟨10.2140/apde.2018.11.1113⟩. ⟨hal-01281469v3⟩
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