Energy and Laplacian of fractal interpolation functions

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 the Sierpinski gasket (SG).As an application,we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1:5 Au=0 on SG{q1,q2,q3},andu(qi) =ai,i=1,2,3,where qi,i=1,2,3,are boundary points of SG.