Let $n\ge2,B=B(0,1)\subset\mathbb{R}^n$ is the unit ball.
Let $u\in C^2(B\backslash\{0\}),\Delta u\le0$ be the super-harmonic function such that $\liminf\limits_{x\to 0}u(x)=0$.
Let $v,w\in C^2(B)$ st. $v,w\le u$ in $B\backslash\{0\}$ and $v(0)=w(0)=0$.
Show that $\nabla v(0)=\nabla w(0)$