Calculus of Variations and Geometric Measure Theory

K. Bessas - M. Novaga - F. Onoue

On the shape of small liquid drops minimizing nonlocal energies

created by bessas on 06 Apr 2023
modified by novaga on 20 Dec 2023


Published Paper

Inserted: 6 apr 2023
Last Updated: 20 dec 2023

Journal: ESAIM Control Optim. Calc. Var.
Volume: 29
Number: Paper n. 86
Pages: 26
Year: 2023
Doi: 10.1051/cocv/2023080

ArXiv: 2304.03255 PDF


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