Uniform convergence rates and Lipschitz regularity estimates in periodic homogenization of high-contrast elliptic systems
Xin Fu, Wenjia Jing · Communications in Partial Differential Equations · 2025
We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions whose conduction parameter exhibits a significant contrast compared to the surrounding matrix media. We develop a unified method to quantify the convergence rates both as the periodicity of inclusions tends to zero and as the contrast approaches either zero or infinity. Based on these convergence rates and an approximation scheme, we also derive Lipschitz regularity estimates that are uniform with respect to both periodicity and contrast.