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 .
Publié le :
Carlo Sbordone 1
@article{CRMATH_2003__337_3_165_0, author = {Carlo Sbordone}, 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}, }
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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