On the <i>Γ</i>-convergence of matrix fields related to the adjugate Jacobian

Carlo Sbordone

doi:10.1016/S1631-073X(03)00280-2

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 Sbordone ¹

¹ Dipartimento di Matematica ed Applicazioni “R. Caccioppoli”, via Cintia, 80126 Napoli, Italy

Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 165-170.

Résumé
Abstract

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 Df_j 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 : 2003-05-13
Publié le : 2003-07-10

DOI : 10.1016/S1631-073X(03)00280-2

Affiliations des auteurs :

Carlo Sbordone ¹

¹ Dipartimento di Matematica ed Applicazioni “R. Caccioppoli”, via Cintia, 80126 Napoli, Italy

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     title = {On the {\protect\emph{\ensuremath{\Gamma}}-convergence} of matrix fields related to the adjugate {Jacobian}},
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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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