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

Abstract

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.