Small perturbation solutions for parabolic equations Yu Wang 35J6035B65Perturbation theoryViscosity solutions. 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. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4961 10.1512/iumj.2013.62.4961 en Indiana Univ. Math. J. 62 (2013) 671 - 697 state-of-the-art mathematics http://iumj.org/access/