Nonlocal energies are continuum models for large systems of particles with long-range interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic kernels?
I will present some results and partial answers in this direction obtained in a long-standing collaboration with Maria Giovanna Mora and Luca Rondi, and with Jose’ Antonio Carrillo, Joan Mateu and Joan Verdera.