A natural approach to the asymptotic mean value property for the $p$-Laplacian

Michinori Ishiwata, Rolando Magnanini, Hidemitsu Wadade

Let $1\le p\le \infty$. We show that a function $u\in C({\mathbb{R}}^N)$ is a viscosity solution to the normalized $p$-Laplace equation ${\Delta }_p^{n}u(x)=0$ if and only if the asymptotic for…