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