Approximating the inverse matrix of the \(G\)-limit through changes of variables in the plane (Q996938)

The authors consider a sequence of coercive symmetric matrices \(A_j\in L^\infty(\mathbb R^2)^{2\times 2}\) with \(\det A_j=1\) which \(G\)--converges to \(A.\) They prove that there exists a sequence of \(K\)--quasiconformal mappings \(F_j\) which converge locally uniformly to a \(K\)--quasiconformal mapping \(F\) such that \(A_j^{-1}\circ F_j^{-1}\) \(G\)--converges to \(A^{-1}\circ F^{-1}.\) The result is specific to the two-dimensional case but a similar result holds in dimension~1.