A counterexample to the pointwise validity of an asymptotic mean value property for $p$-harmonic functions

Ángel Arroyo, Jeff Calder, Mikko Parviainen

We give a counterexample showing that an asymptotic mean value property for $p$-harmonic functions in ${\mathbb{R}}^d$ does not necessarily hold in the pointwise sense for $d\ge 3$ a…