Let $\Omega$ be a bounded open set in $\mathbb{R}^n$ with $C^\infty$ boundary, $n\ge 3$. Define
$$V(z)=\int_\Omega \frac{1}{|z-y|^{n-2}}dy$$
Is it true that $V(z) \in C^{\infty}(\partial \Omega)$?

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Motivation: Classical Holder estimate says that if  $f \in C_c^\alpha(\mathbb{R}^n)$, then the Newtonian potential given by 
$$V(z)=\int_{\mathbb{R}^n} \frac{f(y)}{|z-y|^{n-2}}dy$$
is $C^2$ with respect to $z$ variable. If $f$ is merely bounded, then $V$ is $C^1$ and we cannot expect better regulartiy. This can be seen from the classical example that $f=\chi_{B_1}$, where $\chi$ is the characteristic function and $B_1$ is the unit ball. 

However, for this example, one can see that $V\in C^{\infty}(\partial B_1)$. From this example, it is natural to study the smoothness of $V$ along smooth boundaries. This motivates the original question.