Calculus of Variations and Geometric Measure Theory

M. Cicalese - E. Spadaro

Droplet Minimizers of an Isoperimetric Problem with long-range interactions

created by cicalese on 10 Oct 2011
modified on 21 Dec 2013


Published Paper

Inserted: 10 oct 2011
Last Updated: 21 dec 2013

Journal: Comm. Pure Appl. Math.
Volume: 66
Number: 28
Pages: 1298-1333
Year: 2013


We give a detailed description of the geometry of single droplet patterns in a nonlocal isoperimetric problem. In particular we focus on the sharp interface limit of the Ohta-Kawasaki free energy for diblock copolymers, regarded as a paradigm for those energies modeling physical systems characterized by a competition between short and a long-range interactions. Exploiting fine properties of the regularity theory for minimal surfaces, we extend previous partial results in different directions and give robust tools for the geometric analysis of more complex patterns.