Small Perturbation Solutions for Parabolic Equations
  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. 
Yu Wang
math.AP