Droplet Minimizers of an Isoperimetric Problem with long-range interactions

Details Droplet Minimizers of an Isoperimetric Problem with long-range interactions Droplet Minimizers of an Isoperimetric Problem with long-range interactions

2011-09-30

arxiv.org/abs/1110.0031v1

Mathematics

Analysis of PDEs

24 pages

Scientific paper

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.

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