Variational convergences under moving anisotropies

Abstract

We study the asymptotic behaviour of sequences of integral functionals depending on moving anisotropies. We introduce and describe the relevant functional setting, establishing uniform Meyers-Serrin type approximations, Poincaré inequalities and compactness properties. We prove several $\hat{I}“$-convergence results, and apply the latter to the study of $H$-convergence of anisotropic linear differential operators.