$G$-Convergence of Systems of Generalized Beltrami Equations

Many problems of mathematical physics lead to problems of $G$-convergence of differential operators and, in particular, to the problem of homogenization of partial differential operators. Similar problems arise in elasticity theory, electrodynamics, and other fields of physics and mechanics. In this paper, we consider the problem of $G$-convergence of systems of Beltrami operators. We prove that the class of such systems is $G$-compact and study the properties of $G$-convergence.