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

Abstract

In [3] it is proved that, in some Dirichlet problems, the interplay between the coefficient of the lower order term and the right hand side yields a regularizing effect on the solution: $u$ belongs to $W_0^{1,2}(\Omega )\cap L^{\infty }$ even with a right hand side $f$ belonging only to $L^1(\Omega )$. In this paper we study the role of the interplay assumption under perturbation of the elliptic operator in the sense of the $G$-convergence.