A Remark on the Stability of the Determinant in Bidimensional Homogenization

Farroni, Fernando; Murat, François

Bollettino dell'Unione Matematica Italiana, Tome 3 (2010), p. 209-215 / Harvested from Biblioteca Digitale Italiana di Matematica

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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 $det\,A^{0}=c^{0}$ .

Publié le : 2010-02-01

MR 2605920 | Zbl 1194.35447

@article{BUMI_2010_9_3_1_209_0,
     author = {Fernando Farroni and Fran\c cois Murat},
     title = {A Remark on the Stability of the Determinant in Bidimensional Homogenization},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {3},
     year = {2010},
     pages = {209-215},
     zbl = {1194.35447},
     mrnumber = {2605920},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2010_9_3_1_209_0}
}

Farroni, Fernando; Murat, François. A Remark on the Stability of the Determinant in Bidimensional Homogenization. Bollettino dell'Unione Matematica Italiana, Tome 3 (2010) pp. 209-215. http://gdmltest.u-ga.fr/item/BUMI_2010_9_3_1_209_0/

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