Calculus of Variations and Geometric Measure Theory
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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 02 Jan 2018


Accepted Paper

Inserted: 2 mar 2016
Last Updated: 2 jan 2018

Journal: Anal. PDE
Pages: 29
Year: 2016


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.


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