JournalsrlmVol. 17 , No. 2DOI 10.4171/rlm/461

Approximating the inverse matrix of the G-limit through changes of variables in the plane

  • Gioconda Moscariello

    Università degli Studi di Napoli Federico II, Italy
  • Carlo Sbordone

    Università degli Studi di Napoli Federico II, Italy
  • François Murat

    Université Pierre et Marie Curie, Paris, France
Approximating the inverse matrix of the G-limit through changes of variables in the plane cover

Abstract

Let AjA_j be a sequence of coercive symmetric matrices of L(R2)2×2L^\infty(\mathbb{R}^2)^{2\times 2} with detAj=1det \, A_j=1 which GG-converges to AA. We prove that there exists a sequence of KK-quasiconformal mappings FjF_j which converge locally uniformly to a KK-quasiconformal mapping FF such that Aj1Fj1A_j^{-1}\circ F_j^{-1} GG-converges to A1F1A^{-1}\circ F^{-1}. The result is specific to the two dimensional case but a similar result holds in dimension 11.