ABSTRACT

In this survey talk I will describe my work, joint with Carlos Kenig and Fanghua Lin, on homogenization of elliptic equations and systems. Here we consider a family of second-order elliptic operators with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We obtain uniform sharp regularity estimates of solutions with the Dirichlet or Neumann boundary conditions, as well as sharp convergence rates of solutions and eigenvalues.