  There has been recently an important interest in deriving rigorously the
Cahn-Hilliard equation from the nonlocal equation, also called aggregation
equation. So far, only non-degenerate mobilities were treated. Since we are
motivated by models for the biomechanics of living tissues, it is useful to
include degenerate motilities. In this framework, we present a new method to
show the convergence of the nonlocal to the local degenerate Cahn-Hilliard
equation. The method includes the use of nonlocal Poincar\'e and compactness
inequalities.
