Premium
Droplet Minimizers of an Isoperimetric Problem with Long‐Range Interactions
Author(s) -
Cicalese Marco,
Spadaro Emanuele
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21463
Subject(s) - isoperimetric inequality , limit (mathematics) , focus (optics) , range (aeronautics) , mathematics , energy (signal processing) , mathematical analysis , geometry , physics , optics , materials science , composite material , statistics
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 energies with short‐ and 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. © 2012 Wiley Periodicals inc.