  Hydrodynamic limit for the Ginzburg-Landau $\nabla\phi$ interface model was
established in [Nishikawa, 2003] under the Dirichlet boundary conditions. This
paper studies the similar problem, but with non-convex potentials. Because of
the lack of strict convexity, a lot of difficulties arise, especially, on the
identification of equilibrium states. We give a proof of the equivalence
between the stationarity and the Gibbs property under quite general settings,
and as its conclusion, we complete the identification of equilibrium states
under the high temparature regime in [Deuschel and Cotar, 2008]. We also
establish some uniform estimates for variances of extremal Gibbs measures under
quite general settings.
