Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

Volume constrained minimizers of the fractional perimeter with a potential energy

created by novaga on 27 Feb 2016
modified on 09 Nov 2018


Published Paper

Inserted: 27 feb 2016
Last Updated: 9 nov 2018

Journal: Discrete Contin. Dyn. Syst. S
Volume: 4
Number: 10
Pages: 715-727
Year: 2017

ArXiv: 1602.08612 PDF


We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove existence and regularity of minimizers under suitable assumptions on the potential energy, which cover the periodic case. In the small volume regime we show that minimizers are close to balls, with a quantitative estimate.