Sala Seminari (Dip. Matematica).
We consider a variational model for two interacting species (or phases), subject to cross and self attractive interactions. We show existence and several qualitative properties of minimizers. Depending on the strengths of the attractive forces, minimizers can exhibit different behaviors: phase mixing or phase separation with nested or disjoint phases. For the special case of Coulomb interaction forces, we fully characterize the ground state configurations, by giving its explicit shape. This is a joint work with M. Cicalese, M. Novaga, and M. Ponsiglione.