In this talk, we present the mathematical theory of the homogenisation of composite materials, from its origins in the 1970s to some recent applications. In particular, we discuss a new H-compactness result for possibly non-symmetric and nonlocal linear operators in fractional divergence form. In the second part, we focus on symmetric operators and show that the H-convergence is equivalent to the Gamma-convergence of the associated nonlocal energies.
This research is carried out in collaboration with Maicol Caponi (University of L'Aquila) and Alessandro Carbotti (University of Salento).