Accepted Paper

Inserted: 6 apr 2023
Last Updated: 8 nov 2023

Journal: ESAIM Control Optim. Calc. Var.
Year: 2023

Abstract:

We study the equilibrium shape of liquid drops minimizing the fractional perimeter under the action of a potential energy. We prove, with a quantitative estimate, that the small volume minimizers are convex and uniformly close to a ball.

Keywords: regularity of minimizers, isoperimetric problem, Liquid drop model, Fractional perimeter