MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Droplet minimizers for an isoperimetric problem with long-range interactions

Marco Cicalese and Emanuele Spadaro


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.

Oct 19, 2011
Oct 26, 2011

Related publications

2013 Repository Open Access
Marco Cicalese and Emanuele Spadaro

Droplet minimizers of an isoperimetric problem with long-range interactions

In: Communications on pure and applied mathematics, 66 (2013) 8, pp. 1298-1333