Gradient Estimates for Solutions of Nonparametric Curvature Evolution with Prescribed Contact Angle Condition

where w = √ 1 + |Du|2, ν = (Du/w,−1/w) denotes the downwards directed unit normal on the spatial graph Su of the function u, κ = κ[u] = (κ1, . . . , κn) denotes the n-tuple of principal curvatures of Su with respect to the upward normal, and f is a smooth symmetric function with some special properties as in [1], which is defined in an open convex symmetric cone Γ ⊂ R with vertex at the origin. We assume Γ contains the cone Γ ≡ {κ ∈ R : each component κi > 0} and