Global gradient estimates in directional homogenization

초록

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 Calder on-Zygmund estimates by proving that the gradient of the weak solution is as integrable as the given nonhomogeneous term.

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