A Remark on the Stability of the Determinant in Bidimensional Homogenization

Fernando Farroni; François Murat

Bollettino dell'Unione Matematica Italiana (2010)

  • Volume: 3, Issue: 1, page 209-215
  • ISSN: 0392-4041

Abstract

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For conductivity problems in dimension N = 2, we prove a variant of a classical result: if a sequence A ϵ of matrices H-converges to A 0 (or in other terms if A ϵ converges to A 0 in the sense of homogenization) and if d ⁢ e ⁢ t ⁢ A ϵ tends to c 0 a.e., then one has d ⁢ e ⁢ t ⁢ A 0 = c 0 .

How to cite

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Farroni, Fernando, and Murat, François. "A Remark on the Stability of the Determinant in Bidimensional Homogenization." Bollettino dell'Unione Matematica Italiana 3.1 (2010): 209-215. <http://eudml.org/doc/290687>.

@article{Farroni2010,
abstract = {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 $det \, A^\{0\} = c^\{0\}$.},
author = {Farroni, Fernando, Murat, François},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {209-215},
publisher = {Unione Matematica Italiana},
title = {A Remark on the Stability of the Determinant in Bidimensional Homogenization},
url = {http://eudml.org/doc/290687},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Farroni, Fernando
AU - Murat, François
TI - A Remark on the Stability of the Determinant in Bidimensional Homogenization
JO - Bollettino dell'Unione Matematica Italiana
DA - 2010/2//
PB - Unione Matematica Italiana
VL - 3
IS - 1
SP - 209
EP - 215
AB - 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 $det \, A^{0} = c^{0}$.
LA - eng
UR - http://eudml.org/doc/290687
ER -

References

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