A Remark on the Stability of the Determinant in Bidimensional Homogenization

Farroni, Fernando ; Murat, François

Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 209-215

Résumé

For conductivity problems in dimension N = 2, we prove a variant of a classical result: if a sequence $A^{\epsilon}$ of matrices H-converges to $A^{0}$ (or in other terms if $A^{\epsilon}$ converges to $A^{0}$ in the sense of homogenization) and if $det \, A^{\epsilon}$ tends to $c^{0}$ a.e., then one has $det \, A^{0} = c^{0}$.