Differentiability of minimal surfaces at the boundary

Let Γ be a Jordan curve in R and F(z) = (u(z)9 v(z), w(z)): {\z\ ^ 1} -» R be a solution of Plateau's problem for Γ, where z = x + iy are isothermal parameters. Then u,v,w are harmonic in {\z\ * for | z \ 1, where ω*(t) is a certain modulus of continuity. Once again ω* depends only on Γ.