  Hydrodynamic limit for the Ginzburg-Landau $\nabla\phi$ interface model with
a conservation law was established in [Nishikawa 2002] under the periodic
boundary conditions. This paper studies the same problem on the bounded domain
imposing Dirichlet boundary conditions. A nonlinear partial equation of fourth
order with boundary conditions is derived as the macroscopic equation, which is
related to the Wulff shape derived by [Deuschel et.al. 2000].
