  The mixed form of the Cahn-Hilliard equations is discretized by the
hybridizable discontinuous Galerkin method. For any chemical energy density,
existence and uniqueness of the numerical solution is obtained. The scheme is
proved to be unconditionally stable. Convergence of the method is obtained by
deriving a priori error estimates that are valid for the Ginzburg-Lindau
chemical energy density and for convex domains. The paper also contains
discrete functional tools, namely discrete Agmon and Gagliardo-Nirenberg
inequalities, which are proved to be valid in the hybridizable discontinuous
Galerkin spaces.
