A remark on infinity-harmonic functions.

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Tug-of-war and the infinity Laplacian (2006, background): “Crandall and Evans [10] have explored the following question in some detail, and it has recently been answered aﬃrmatively by Savin [23] when n = 2: is every ∞ - harmonic function on a domain in R n everywhere diﬀerentiable?”
A TOUR OF THE THEORY OF ABSOLUTELY MINIMIZING FUNCTIONS (2004, methodology): “Evans noticed the convexity of g during the preparation of [30], although no use was made of it at that time.”
Inhomogeneous infinity Laplace equation (2008, background): “A function f :S → R is said to be Lipschitz continuous on S if there is a constant L such that ∣∣f (x) − f (y)∣∣ L|x − y|, for any x and y in S.”
Nonlocal Tug‐of‐War and the Infinity Fractional Laplacian (2010, result): “The strategy is similar to the blow-up arguments employed in [7, 8].”