Large deviations for the Ginzburg-Landau ∇ φ interface model

Hydrodynamic large scale limit for the Ginzburg-Landau ∇φ interface model was established in [6]. As its next stage this paper studies the corresponding large deviation problem. The dynamic rate functional is given by I (h) = 1/4 (latin small letter esh)^T₀ dt (latin small letter esh)double struck T sign d {∂h/∂t - div (∇σ (Vh))}² dθ for h = h(t, θ), t ∈ [0, T], θ ∈ double struck T^d, where σ = σ (u) is the surface tension for mean tilt u ∈ double struck R^d. Our main tool is H^-1-method exploited by Landim and Yau [9]. The relationship to the rate functional obtained under the static situation by Deuschel et al. [3] is also discussed.