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

Hydrodynamic limit for the Ginzburg-Landau $\nabla\phi$ interface model with non-convex potential