Homogenization in Perforated Domains and Interior Lipschitz Estimates
  We establish interior Lipschitz estimates at the macroscopic scale for
solutions to systems of linear elasticity with rapidly oscillating periodic
coefficients and mixed boundary conditions in domains periodically perforated
at a microscopic scale $\varepsilon$ by establishing $H^1$-convergence rates
for such solutions. The interior estimates are derived directly without the use
of compactness via an argument presented in [3] that was adapted for elliptic
equations in [2] and [11]. As a consequence, we derive a Liouville type
estimate for solutions to the systems of linear elasticity in unbounded
periodically perforated domains.
