Preprint 70/2011

Droplet minimizers for an isoperimetric problem with long-range interactions

Marco Cicalese and Emanuele Spadaro

Contact the author: Please use for correspondence this email.
Submission date: 19. Oct. 2011
Pages: 26
published in: Communications on pure and applied mathematics, 66 (2013) 8, p. 1298-1333 
DOI number (of the published article): 10.1002/cpa.21463
with the following different title: Droplet minimizers of an isoperimetric problem with long-range interactions
Download full preprint: PDF (454 kB)

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.

16.02.2021, 02:14