Various Properties of Solutions of the Infinity-Laplacian Equation

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Tug-of-war and the infinity Laplacian (2006, background): “Numerical calculations [21] had suggested that in the setting of the theorem ω∞(Aδ) tends to 0 as δ → 0, but this was only recently proved [ 12 ], and the proof did not yield any quantitative information on the rate of decay.”
C1,α regularity for infinity harmonic functions in two dimensions (2008, methodology): “Furthermore, some observations in [ 3 ]a nd [2] suggest that u is in fact differentiable everywhere.”