Sunghan Kim: Higher order convergence rate in periodic homogenization for equations in non-divergence form

In this talk, I will address recent achievement in higher order convergence rate in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile. This is a joint work with Ki-Ahm Lee.