Calculus of Variations and Geometric Measure Theory

M. Goldman - M. Novaga - B. Ruffini

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

created by ruffini on 02 Mar 2016
modified by novaga on 13 Apr 2018


Published Paper

Inserted: 2 mar 2016
Last Updated: 13 apr 2018

Journal: Anal. PDE
Volume: 11
Number: 5
Pages: 1113–1142
Year: 2018


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 in finity.