In this talk, we introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain and complemented with homogeneous Dirichlet boundary conditions of solid type. After briefly showing how to prove existence and uniqueness, we investigate the convergence of solutions for this class of nonlocal Cahn-Hilliard problems to their local counterparts, as the order of the fractional Laplacian appearing in the equation is let tend to 1.
