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, Tome 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
Sbordone, Carlo 1

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

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

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

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

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

Cité par Sources :