An asymptotic mean value characterization for p-harmonic functions

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Harnack's Inequality for p-Harmonic Functions via Stochastic Games (2012, background): “Fix > 0 and consider the following two-player zero-sum-game from [18], see also [16] and [17].”
A New Proof for the Equivalence of Weak and Viscosity Solutions for the p-Laplace Equation (2011, methodology): “The equivalence has turned out to be a very useful tool in certain removability questions, see [7, 13], as well as in the analysis of various approximations of the p-Laplace equation see [4, 11, 12].”
Games for eigenvalues of the Hessian and concave/convex envelopes (2018, background): “For a mean value property for the p − Laplacian we refer to [9] and [8].”
On the definition and properties of p-harmonious functions (2012, methodology): “To accomplish this, we utilize some ideas from [11], where p-harmonic functions were characterized in terms of asymptotic expansions.”
Solutions of nonlinear PDEs in the sense of averages (2012, methodology): “First we recall a calculation from [19] leading to an asymptotic expansion involving the infinity Laplacian.”
On the existence and uniqueness of $p$-harmonious functions (2012, background): “1) in the asymptotic sense as in [MPR10b], it actually characterizes the viscosity solutions to the p-Laplace equation when p > 1.”