Slope estimate and boundary differentiability of infinity harmonic functions on convex domains. (July 2016) - Hong, Guanghao; Liu, Dawei
Abstract: We study the boundary differentiability of infinity harmonic functions with given differentiable boundary data on convex domains. At a flat point (the boundary point where the blow-up of the domain is the half-space), the infinity harmonic function u is differentiable due to a previous result of the first author in Hong (2013). At a corner point (the boundary point where the blow-up of the domain is not the half-space), an example shows that u is not necessarily differentiable. In this paper, we establish a slope estimate for u at corner points and provide a necessary and sufficient condition for the differentiability of u at corner points.