  In this paper, we first characterize the finiteness of fractal interpolation
functions (FIFs) on post critical finite self-similar sets. Then we study the
Laplacian of FIFs with uniform vertical scaling factors on Sierpinski gasket
(SG). As an application, we prove that the solution of the following Dirichlet
problem on SG is an FIF with uniform vertical scaling factor $\frac{1}{5}$:
$\Delta u=0$ on $SG\setminus \{q_1,q_2,q_3\}$, and $u(q_i)=a_i$, $i=1,2,3$,
where $q_i$, $i=1,2,3$, are boundary points of SG.
