  We establish optimal conditions under which the G-convergence of linear
elliptic operators implies the convergence of the corresponding Dirichlet to
Neumann maps. As an application we show that the approximate cloaking isotropic
materials from [ Greenleaf, A.; Kurylev, Y.; Lassas, M.; Uhlmann, G.
Approximate quantum and acoustic cloaking. J. Spectr. Theory (2011), no. 1,
27--80.] are independent of the source.
