Title: Self-improvement properties for nonlocal equations

Abstract:  I will present some results related to generalization of Meyers result to nonlocal equation. It happens that any weak solution of a nonlocal equation with data in L2 is automatically better at the integrability AND differentiability scale. This is a completely new phenomenon relying on the nonlocality of the operator. The proof is based on a new stopping time argument and a suitable generalization of Gehring lemma.