On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint
arXiv:1603.01240 · doi:10.2140/apde.2018.11.1113
Abstract
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.