JournalsrlmVol. 17, No. 2pp. 167–174

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
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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.

Cite this article

Gioconda Moscariello, Carlo Sbordone, François Murat, Approximating the inverse matrix of the G-limit through changes of variables in the plane. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 2, pp. 167–174

DOI 10.4171/RLM/461