The infinity Laplacian, Aronsson’s equation and their generalizations

By E. Barron, Lawrence C. Evans, R. Jensen. 2008

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A finite difference approach to the infinity Laplace equation and tug-of-war games (2009, methodology): “As a second application of Proposition 5.3, we give a simple proof of Jensen’s theorem on the uniqueness of infinity harmonic functions.”
Nonlocal Tug‐of‐War and the Infinity Fractional Laplacian (2010, background): “There are many variations on the rules of the game, for example adding a running cost of movement, which give rise to a class of related “Aronsson equations”, see [1, 11, 12].”
An asymptotic mean value characterization for p-harmonic functions (2010, background): “The infinity Laplacian appears naturally when one considers limits as p → ∞ of p-harmonic functions in the viscosity sense and has applications to best Lipschitz extensions, image processing and mass transport problems; see [2], [3], [4], [7], [8], [9].”
A deterministic‐control‐based approach to fully nonlinear parabolic and elliptic equations (2010, background): “Until recently, the only control-based interpretations of second-order elliptic or parabolic equations involved stochasticity.”
On the Structure of ∞-Harmonic Maps (2014, methodology): “was first derived and studied by Aronsson in the ’60s in [3, 4] and has been extensively studied ever since (see for example Crandall [11], Barron-Evans-Jensen [8] and references therein).”