  In this paper, we apply blow-up analysis and Liouville type theorems to study
pointwise a priori estimates for some quasilinear equations with p-Laplace
operator. We first obtain pointwise interior estimates for the gradient of
p-harmonic function, i.e., the solution of $\Delta_{p}u=0,\ x\in\Omega$, which
extends the well-established results of the interior estimates of the gradient
of harmonic function. We then get singularity and decay estimates of the sign
changing solution of Lane-Emden-Fowler type p-Laplace equation
$-\Delta_{p}u=|u|^{\lambda-1}u, \ x\in\Omega$, which are then generalized for
the equation with general right hand term $f(x,u)$, under some asymptotic
conditions of $f$. Lastly, we get pointwise estimates for higher order
derivatives of the solution of $-\Delta u=u^{\lambda},x\in\Omega$, the case of
$p=2$ for p-Laplace equation.
