Inserted: 30 jul 2015
Last Updated: 29 oct 2016
Journal: SIAM J. Math. Anal.
We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, dierent behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state congurations.
Keywords: Variational methods, shape optimization, nonlocal interactions, Coulomb interactions