Mean value property for 𝑝-harmonic functions
Tiziana Giorgi, Robert G. Smits · Proceedings of the American Mathematical Society · 2011
We derive a mean value property for p p -harmonic functions in two dimensions, 1 > p > ∞ 1>p>\infty , which holds asymptotically in the viscosity sense. The formula coincides with the classical mean value property for harmonic functions, when p = 2 p=2 , and is a consequence of a representation for the Game p p -Laplacian obtained via p p -averaging.