## Analysis & PDE

• Anal. PDE
• Volume 11, Number 5 (2018), 1113-1142.

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

#### Abstract

We study a variational problem modeling the behavior at equilibrium of charged liquid drops under a convexity constraint. After proving the 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.

#### Article information

Source
Anal. PDE, Volume 11, Number 5 (2018), 1113-1142.

Dates
Revised: 6 July 2017
Accepted: 2 January 2018
First available in Project Euclid: 17 April 2018

https://projecteuclid.org/euclid.apde/1523930416

Digital Object Identifier
doi:10.2140/apde.2018.11.1113

Mathematical Reviews number (MathSciNet)
MR3785601

Zentralblatt MATH identifier
06866544

#### Citation

Goldman, Michael; Novaga, Matteo; Ruffini, Berardo. On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint. Anal. PDE 11 (2018), no. 5, 1113--1142. doi:10.2140/apde.2018.11.1113. https://projecteuclid.org/euclid.apde/1523930416

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