Mean value properties for p-harmonic functions for higher dimensions

Mean value theorems play a fundamental role in the understanding of elliptic partial differential equations, both for existence and uniqueness. For the classical Laplacian they are also invoked to understand the local behavior of functions. There has been a number of results generalizing this to the p-Laplacian, in 2 dimensions for the p-average and for all dimensions for other types of averages. Here we extend previous results to higher dimensions with a view to numerics in higher dimensions based on game theory.