For a family of systems of linear elasticity with rapidly oscillating periodic
coefficients, we establish sharp boundary estimates with either Dirichlet or
Neumann conditions, uniform down to the microscopic scale, without smoothness
assumptions on the coefficients. Under additional smoothness conditions, these
estimates, combined with the corresponding local estimates, lead to the
full Rellich-type estimates in Lipschitz domains and Lipschitz estimates in
domains.
The
,
, and
estimates in
domains
for systems with VMO coefficients are also studied. The approach is based on
certain estimates on convergence rates. As a biproduct, we obtain sharp
error estimates
in
for
and a Lipschitz
domain
,
with no smoothness assumption on the coefficients.
Keywords
homogenization, systems of elasticity, convergence rates,
Rellich estimates, Lipschitz estimates
