Directional homogenization of elliptic equations in non-divergence form

Abstract

The paper concerns regularities of solutions of elliptic equations in non-divergence form with directional homogenization. The main interest is to investigate the differences of regularities of datums that are needed and of solutions that are obtained between directions with homogenization and without homogenization. We establish uniform interior Lp(1<p≤∞) estimates for D2uε and uniform interior Cγ(0≤γ<1) estimates for DDx′uε, where x′ are the non-homogenization directions. Our results are optimal.