Small Perturbation Solutions for Parabolic Equations
Yu Wang · arXiv (Cornell University) · 2011
Let $ϕ$ 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 $(D^2ϕ, Dϕ, ϕ, x, t)$, we prove that any solution obtained from small L1-perturbation of $ϕ$ remains smooth.