[Sur la Γ-convergence de champs de matrices relatifs au jacobien adjugué]
La transposée des cofacteurs de la matrice jacobienne de l'application peut être exprimée en fonction de la matrice jacobienne : , pour , en utilisant une matrice symétrique telle que p.p. Sous des hypothèses appropriées, nous prouvons que Dfj converge faiblement vers Df dans si et seulement si Γ-converge vers une matrice telle que p.p. et vérifiant .
Adjugate Jacobians of mappings can be represented in terms of Jacobian matrices: , for , by mean of symmetric matrix fields with a.e. Under suitable conditions, we prove that weakly in if and only if Γ-converges to a matrix with satisfying .
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@article{CRMATH_2003__337_3_165_0,
author = {Sbordone, Carlo},
title = {On the {\protect\emph{\ensuremath{\Gamma}}-convergence} of matrix fields related to the adjugate {Jacobian}},
journal = {Comptes Rendus. Math\'ematique},
pages = {165--170},
publisher = {Elsevier},
volume = {337},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00280-2},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00280-2/}
}
TY - JOUR AU - Sbordone, Carlo TI - On the Γ-convergence of matrix fields related to the adjugate Jacobian JO - Comptes Rendus. Mathématique PY - 2003 SP - 165 EP - 170 VL - 337 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00280-2/ DO - 10.1016/S1631-073X(03)00280-2 LA - en ID - CRMATH_2003__337_3_165_0 ER -
%0 Journal Article %A Sbordone, Carlo %T On the Γ-convergence of matrix fields related to the adjugate Jacobian %J Comptes Rendus. Mathématique %D 2003 %P 165-170 %V 337 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00280-2/ %R 10.1016/S1631-073X(03)00280-2 %G en %F CRMATH_2003__337_3_165_0
Sbordone, Carlo. On the Γ-convergence of matrix fields related to the adjugate Jacobian. Comptes Rendus. Mathématique, Tome 337 (2003) no. 3, pp. 165-170. doi : 10.1016/S1631-073X(03)00280-2. http://www.numdam.org/articles/10.1016/S1631-073X(03)00280-2/
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