Comptes Rendus
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]
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/

[1] C. Capone Quasiharmonic fields and Beltrami operators, Comment. Math. Univ. Carolinae, Volume 43 (2002) no. 2, pp. 363-377

[2] R. De Arcangelis; P. Donato On the convergence of Laplace–Beltrami operators associated to quasiregular mappings, Studia Math., Volume 86 (1987) no. 3, pp. 189-204

[3] L. D'Onofrio, L. Greco, A counterexample in G-convergence of nondivergence elliptic operators, Preprint, 2003

[4] T. Iwaniec; G. Martin Geometric Function Theory and Non-Linear Analysis, Oxford Math. Monographs, Oxford University Press, 2001

[5] T. Iwaniec, C. Sbordone, G-convergence of Beltrami operators, in press

[6] P. Marcellini; C. Sbordone An approach to the asymptotic behaviour of elliptic–parabolic operators, J. Math. Pures Appl. (9), Volume 56 (1977) no. 2, pp. 157-182

[7] F. Murat; L. Tartar H-Convergence. Topics in the Mathematical Modelling of Composite Materials, Progr. Nonlinear Differential Equations Appl., 31, Birkhäuser, Boston, 1997 (pp. 21–43)

[8] Yu.G. Reshetnyak Mappings of bounded deformations as extremals of Dirichlet type integrals, Sibirsk. Mat. Zh., Volume 9 (1968), pp. 625-666

[9] C. Sbordone, On the convergence of the associated matrix to the adjugate Jacobian, 2003, in press

[10] S. Spagnolo Some convergence problems, Symposia Mathematica, Vol. XVIII (Convegno sulle Transformazioni Quasiconformi e Questioni Connesse, INDAM, Rome, 1974), 1976, pp. 391-398

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