Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model with boundary conditions

Hydrodynamic limit for the Ginzburg-Landau ∇φ interface model was established in [6] under periodic boundary conditions. This paper studies the same problem on a bounded domain imposing Dirichlet boundary conditions. A nonlinear partial differential equation of second order with boundary conditions is derived as a macroscopic equation. The main tools are H − 1-method used in [6] and the higher integrability of gradients in [2].