Boundary differentiability of infinity harmonic functions

We prove that an infinity harmonic function u(x)∈C(Ω̄) is differentiable at a boundary point x0∈∂Ωx0∈∂Ω if both ∂Ω∂Ω and the boundary data g(x)g(x) are differentiable at x0x0. This work improved a former result of Changyou Wang and Yifeng Yu (2012)  [10]. They obtained the boundary differentiability of u(x)u(x) with the C1C1 assumption on ∂Ω∂Ω and g(x)g(x).