On the periodic homogenization of elliptic equations in non-divergence form with large drifts

Abstract

We study the quantitative homogenization of linear second order elliptic equations in non-divergence form with highly oscillating periodic diffusion coefficients and with large drifts, in the so-called ``centered'' setting where homogenization occurs and the large drifts contribute to the effective diffusivity. Using the centering condition and the invariant measures associated to the underlying diffusion process, we transform the equation into divergence form with modified diffusion coefficients but without drift. The latter is in the standard setting for which quantitative homogenization results have been developed systematically. An application of those results then yields quantitative estimates, such as the convergence rates and uniform Lipschitz regularity, for equations in non-divergence form with large drifts.