Slope estimate and boundary differentiability for inhomogeneous infinity Laplace equation on convex domains

We study the boundary differentiability for inhomogeneous infinity Laplace equations on convex domains Ω with the inhomogeneous term f∈C(Ω)∩L∞(Ω) and differentiable boundary data g. At a flat point (the boundary point where the blow up of the domain is the half-space), u is differentiable due to a previous result of the second author in Hong (2014). At a corner point (the boundary point where the blow up of the domain is not the half-space), we establish a slope estimate for u, and provide a necessary and sufficient condition for the boundary differentiability of u in this paper.