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 $|f(x)|\le Qa(x)$.