  Let $\phi$ be a smooth solution of the parabolic equation $F(D^2u, Du, u, x,
t)- u_{t} = 0$: Assume $F$ is uniform elliptic only in a neighborhood of
$(D^2\phi, D\phi, \phi, x, t)$, we prove that any solution obtained from small
L1-perturbation of $\phi$ remains smooth.
