Some estimates from homogenized elasticity problems

L2- and H1-estimates for elasticity problems were studied in the whole space or a bounded domain, including perforated ones. Various spaces of vector functions were employed, but they are frequently denoted as usual scalar spaces. An elasticity system in the whole space was analyzed in vector form as a function of measurable periodic elasticity tensor that satisfies the usual symmetry conditions and the ellipticity condition. The analysis showed that there exists a substantial difference between scalar and elasticity problems with respect to the approximation theory.