The role of interplay between coefficients in the $G$-convergence of some elliptic equations

Abstract

We study the behavior of the solutions $u$ of the linear Dirichlet problems $- \mathrm{div} (M(x) \nabla u) + a(x) u = f(x)$ with respect to perturbations of the matrix $M(x)$ (with respect to the $G$-convergence) and with respect to perturbations of the nonnegative coefficient $a(x)$ and of the right hand side $f(x)$ satisfying the condition $|f (x)| \leq Q \, a (x)$.