@article{D'Elia2022, 
author = {Lorenza D'Elia},
title = {Γ-convergence of quadratic functionals with non uniformly elliptic conductivity matrices},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {1},
pages = {15-45},
keywords = {Quadratic functionals, homogenization, Γ-convergence, two-scale convergence, non-local functional},
url = {https://www.sciopen.com/article/10.3934/nhm.2021022},
doi = {10.3934/nhm.2021022},
abstract = {We investigate the homogenization through    Γ-convergence for the        L    2    (      Ω    )-weak topology of the conductivity functional with a zero-order term where the matrix-valued conductivity is assumed to be non strongly elliptic. Under proper assumptions, we show that the homogenized matrix        A    ∗   is provided by the classical homogenization formula. We also give algebraic conditions for two and three dimensional    1-periodic rank-one laminates such that the homogenization result holds. For this class of laminates, an explicit expression of        A    ∗   is provided which is a generalization of the classical laminate formula. We construct a two-dimensional counter-example which shows an anomalous asymptotic behaviour of the conductivity functional.}
}