  In this note, we investigate the regularity of extremal solution $u^*$ for
semilinear elliptic equation $-\triangle u+c(x)\cdot\nabla u=\lambda f(u)$ on a
bounded smooth domain of $\mathbb{R}^n$ with Dirichlet boundary condition. Here
$f$ is a positive nondecreasing convex function, exploding at a finite value
$a\in (0, \infty)$. We show that the extremal solution is regular in low
dimensional case. In particular, we prove that for the radial case, all
extremal solution is regular in dimension two.
