IUMJ

Title: Small perturbation solutions for parabolic equations

Authors: Yu Wang

Issue: Volume 62 (2013), Issue 2, 671-697

Abstract:

Let $\varphi$ be a smooth solution of the parabolic equation \[ F(D^2u,Du,u,x,t)-u_t=0. \] Assume that $F$ is smooth and uniformly elliptic only in a neighborhood of the points $(\DD^2\varphi,D\varphi,\varphi,x,t)$. Then, we show that a viscosity solution $u$ to the above equation is smooth in the interior if $\|u-\varphi\|_{L^{\infty}}$ is sufficiently small.