C. Amrouche and V. Girault, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J, vol.44, pp.109-140, 1994.

M. Bellieud and G. Bouchitté, Homogenization of elliptic problems in a fiber reinforced structure. Nonlocal effects, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.26, pp.407-436, 1998.
URL : https://hal.archives-ouvertes.fr/hal-01283228

M. E. Bogovski, Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl, vol.20, pp.1094-1098, 1979.

J. Bourgain and H. Brezis, New estimates for elliptic equations and Hodge type systems, Journal of the European Mathematical Society, vol.9, pp.277-315, 2007.
DOI : 10.4171/JEMS/80

H. Brezis, Analyse Fonctionnelle, Théorie et Applications. Mathématiques Appliquées pour la Ma??triseMa??trise, 1983.

H. Brezis and J. Van-schaftingen, Boundary estimates for elliptic systems with L1???data, Calculus of Variations and Partial Differential Equations, vol.35, issue.1, pp.369-388, 2007.
DOI : 10.1016/j.crma.2004.05.013

M. Briane, Homogenization of the Stokes equations with high-contrast viscosity, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.7, pp.843-876, 2003.
DOI : 10.1016/S0021-7824(03)00012-6

M. Briane and J. C. Díaz, Compactness of sequences of two-dimensional energies with a zero-order term. Application to three-dimensional nonlocal effects, Calculus of Variations and Partial Differential Equations, vol.22, issue.3, pp.463-492, 2008.
DOI : 10.1016/S0021-7824(97)89958-8
URL : https://hal.archives-ouvertes.fr/hal-00359993

M. Camar-eddine and P. Seppecher, Determination of the Closure of the Set of Elasticity Functionals, Archive for Rational Mechanics and Analysis, vol.170, issue.3, pp.211-245, 2003.
DOI : 10.1007/s00205-003-0272-7

G. De-rham, Variétés différentiables, Formes, courants, formes harmoniques, 1973.

D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order [12] E. Hopf, ¨ Uber die Anfwangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr, vol.4, pp.213-231, 1951.

E. Y. Khruslov, Homogenized Models of Composite Media, Composite Media and Homogenization Theory Progress in Nonlinear Differential Equations and Their Applications, pp.159-182, 1991.
DOI : 10.1007/978-1-4684-6787-1_10

O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Mathematics and its Applications 2. Gordon and Breach, Science Publishers, 1969.

J. Lions, Quelques résultats d'existence dans deséquationsdeséquations aux dérivées partielles non linéaires, Bull. S.M.F, vol.87, pp.245-273, 1959.

V. A. Marchenko and E. Y. Khruslov, Homogenization of partial differential equations, Progress in Mathematical Physics 46. Birkhäuser, 2006.

C. Pideri and P. Seppecher, A second gradient material resulting from the homogenization of an heterogeneous linear elastic medium, Continuum Mechanics and Thermodynamics, vol.9, issue.5, pp.241-257, 1997.
DOI : 10.1007/s001610050069
URL : https://hal.archives-ouvertes.fr/hal-00527291

M. Strauss, Variations of Korn's and Sobolev's inequalities, Partial Differential Equations: Proc. Symp. Pure Math, pp.207-214, 1973.

L. Tartar, Topics in nonlinear analysis, p.271, 1978.

R. Temam, Navier Stokes Equations: Theory and Numerical Analysis, Studies in Mathematics and its Applications, 1984.
DOI : 10.1115/1.3424338

J. Van-schaftingen, Estimates for L1-vector fields under higher-order differential conditions, Journal of the European Mathematical Society, vol.10, pp.867-882, 2008.
DOI : 10.4171/JEMS/133

J. Van-schaftingen, Estimates for L1-vector fields, Comptes Rendus Mathematique, vol.339, issue.3, pp.181-186, 2004.
DOI : 10.1016/j.crma.2004.05.013