Droplet minimizers for an isoperimetric problem with long-range interactions

Marco Cicalese and Emanuele Spadaro

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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
Bibtex
with the following different title: Droplet minimizers of an isoperimetric problem with long-range interactions
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Abstract:
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.