Elliptic homogenization with almost translation-invariant coefficients
Rémi Goudey · arXiv (Cornell University) · 2022
We consider an homogenization problem for the second order elliptic equation $-\operatorname{div}\left(a(./\varepsilon) abla u^{\varepsilon} \right)=f$ when the coefficient $a$ is almost translation-invariant at infinity and models a geometry close to a periodic geometry. This geometry is characterized by a particular discrete gradient of the coefficient $a$ that belongs to a Lebesgue space $L^p(\mathbb{R}^d)$ for $p\in[1,+\infty[$. When $p