Convergence rate and uniform Lipschitz estimate in periodic homogenization of high-contrast elliptic systems

We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions whose conduction parameter exhibits a significant contrast compared to the background media. We develop a unified method to quantify the convergence rates both as the periodicity of inclusions tends to zero and as the parameter approaches either zero or infinity. Based on the obtained convergence rates and a Campanato-type scheme, we also derive the regularity estimates that are uniform both in the periodicity and the contrast.