Aperiodic fractional obstacle problems

We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Gamma-convergence arguments. As further developments we consider obstacles with random sizes and shapes located on points of standard lattices, and the case of random homothetics obstacles centred on random Delone sets of points. Obstacle problems for non-local energies occur in several physical phenomena, for which our results provide a description of the zeroth order asymptotic behaviour.