In a physical system which involves competing long-range and short-range interactions, one heuristically expects the formation of patterns (or some kind of periodicity). I will present a simple variational model, derived from the Ohta-Kawasaki model for block copolymers, and show how one can prove that the energy of minimizers is uniformly distributed at large scales; a necessary condition for the existence of patterns.
This talk will be based on a recent joint work with Katarina Bellova et Felix Otto, and on a paper by Giovani Alberti, Rustum Choksi and Felix Otto about a similar system.
Clément Sarrazin
