Low density phases in a uniformly charged liquid

We consider a macroscopic limit for the Ohta-Kawasaki energy. This model has been used to described to describe phase separation for diblock-copolymers. We first investigate existence and shape of minimizers of the energy with prescribed volume (of the one phase) in the full space setting. We then consider situation of periodic configurations with prescribed density of the minority phase. We show that in a certain regime, the energy Gamma-converges to a homogenized problem. This is joint work with C. Muratov and M. Novaga.