$H^0$ ‐convergence for the linearized elasticity system

In Nonlinear Partial Differential Equations and Their Applications, Vol. 13 (to appear), Briane, Damlamian and Donato extend to the case of perforated domains the $H$ ‐covergence introduced by Murat and Tartar (Sém. Anal. Fonct. Numér., 1977/1978; Topics in the Mathematical Modelling of Composite Materials, 1997) for the diffusion equation.

In this paper, we define in the same spirit a notion of $H^0$ ‐convergence for the linearized elasticity system in perforated domains. This definition allows to obtain compactness, locality and corrector results.