RECENT PROGRESS IN THE THEORY OF HOMOGENIZATION WITH OSCILLATING DIRICHLET DATA

摘要

In this paper we study the homogenization of elliptic systems with Dirichlet boundary condition, when both the coefficients and the boundary datum are oscillating, namely ε-periodic. In particular, in the paper [9], we showed that, as ε → 0, the solutions converge in L~2 with a power rate in ε, and we identified the homogenized limit system and the homogenized boundary data. Due to a boundary layer phenomenon, this homogenized system depends in a non trivial way on the boundary. The analysis in [9] answers a longstanding open problem, raised for instance in [4].