MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Droplet minimizers for an isoperimetric problem with long-range interactions
Marco Cicalese and Emanuele SpadaroAbstract
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.
- Received:
- 19.10.11
- Published:
- 26.10.11