Approximating the inverse matrix of the G-limit through changes of variables in the plane
Gioconda Moscariello, Carlo Sbordone, François Murat · Rendiconti Lincei Matematica e Applicazioni · 2006
Let A_j be a sequence of coercive symmetric matrices of L^\infty(\mathbb{R}^2)^{2\times 2} with det \, A_j=1 which G -converges to A . We 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 .