  We establish pointwise a priori estimates for solutions in
$D^{1,p}(\mathbb{R}^n)$ of equations of type $-\Delta_pu=f(x,u)$, where
$p\in(1,n)$, $\Delta_p:=\mbox{div}\big(\left|\nabla u\right|^{p-2}\nabla
u\big)$ is the $p$-Laplace operator, and $f$ is a Caratheodory function with
critical Sobolev growth. In the case of positive solutions, our estimates allow
us to extend previous radial symmetry results. In particular, by combining our
results and a result of Damascelli-Ramaswamy, we are able to extend a recent
result of Damascelli-Merch\'an-Montoro-Sciunzi on the symmetry of positive
solutions in $D^{1,p}(\mathbb{R}^n)$ of the equation $-\Delta_pu=u^{p^*-1}$,
where $p^*:=np/(n-p)$.
