Global gradient estimates in directional homogenization

Abstract

In this research, we investigate a higher regularity result in periodic directional homogenization for divergence-form elliptic systems with discontinuous coefficients in a bounded nonsmooth domain. The coefficients are assumed to have small bounded mean oscillation (BMO) seminorms and the domain has the $ \delta $-Reifenberg property. Under these assumptions we derive global uniform Calderón-Zygmund estimates by proving that the gradient of the weak solution is as integrable as the given nonhomogeneous term.

Keywords

• directional homogenization
• uniform estimate
• calderón-zygmund theory
• reifenberg domain
• bmo coefficient