Linear elliptic homogenization for a class of highly oscillating non-periodic potentials

Abstract

We consider an homogenization problem for the second order elliptic equation $-\Delta u^{\epsilon }+\frac{1}{\epsilon }V(./\epsilon )u^{\epsilon }+\nu u^{\epsilon }=f$ when the highly oscillatory potential $V$ belongs to a particular class of non-periodic potentials. We show the existence of an adapted corrector and prove the convergence of $u^{\epsilon }$ to its homogenized limit.

39 pages, 3 figures