2000 character limit reached
On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint (1603.01240v2)
Published 3 Mar 2016 in math.AP
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.