A closure theorem for gAMMA-convergence and H-convergence with applications to non-periodic homogenization
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Date
2024-02-29
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Abstract
In this work we examine the stability of some classes of integrals, and in particular
with respect to homogenization. The prototypical case is the homogenization of
quadratic energies with periodic coe cients perturbed by a term vanishing at in nity,
which has been recently examined in the framework of elliptic PDE.We use localization
techniques and higher-integrability Meyers-type results to provide a closure theorem by
gamma-convergence within a large class of integral functionals. From such result we derive
stability theorems in homogenization which comprise the case of perturbations with
zero average on the whole space. The results are also extended to the stochastic case,
and specialized to the G-convergence of operators corresponding to quadratic forms. A
corresponding analysis is also carried on for non-symmetric operators using the localization
properties of H-convergence. Finally, we treat the case of perforated domains
with Neumann boundary condition, and their stability.
Description
SISSA 3/2024/MATE