Homogenization of Dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design

In a previous paper, we studied the homogenization of a sequence of parabolic linear Dirichlet problems, when the coefficients and the domains vary arbitrarily. Here, we improve the convergence result given in this paper by showing the strong convergence in L 2 every time. This is applied to obtain an existence result for control problems in optimal design written in a relaxed form. The control variables are the material and the shape.