Recent progress in the theory of homogenization with oscillating Dirichlet data

Abstract

This note is a summary of the recent paper [9]. Here, we study the homogenization of elliptic systems with Dirichlet boundary condition, when both the coefficients and the boundary datum are oscillating. In particular, in the paper [9], we showed that, the solutions converge in L2 with a power rate, 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]

References in corpus (6)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• Convergence Rates in L^2 for Elliptic Homogenization Problems
• Homogenization of the boundary value for the Dirichlet Problem
• Homogenization of Elliptic Systems with Neumann Boundary Conditions
• Homogenization of Green and Neumann Functions
• Applications of Fourier analysis in homogenization of Dirichlet problem II. $L^p$ estimates