Comptes Rendus
no. 3
Partial Differential Equations
On the Γ-convergence of matrix fields related to the adjugate Jacobian
[Sur la Γ-convergence de champs de matrices relatifs au jacobien adjugué]

Présenté par : Haïm Brezis

Carlo Sbordone1
1 Dipartimento di Matematica ed Applicazioni “R. Caccioppoli”, via Cintia, 80126 Napoli, Italy
Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 165-170.

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 .

Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00280-2
Carlo Sbordone 1

1 Dipartimento di Matematica ed Applicazioni “R. Caccioppoli”, via Cintia, 80126 Napoli, Italy 
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Carlo Sbordone. On the Γ-convergence of matrix fields related to the adjugate Jacobian. Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 165-170. doi : 10.1016/S1631-073X(03)00280-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00280-2/

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