R. A. Adams, Sobolev spaces Academic Press [A subsidiary of Harcourt Brace Jovanovich , Publishers], Pure and Applied Mathematics, vol.65, 1975.

S. N. Armstrong and Z. Shen, Lipschitz Estimates in Almost-Periodic Homogenization, Communications on Pure and Applied Mathematics, vol.57, issue.5
DOI : 10.1512/iumj.2008.57.3344
URL : https://hal.archives-ouvertes.fr/hal-01483384

S. N. Armstrong and C. K. Smart, Quantitative stochastic homogenization of convex integral functionals, Ann. Sci. ´ Ec. Norm. Supér. to appear
URL : https://hal.archives-ouvertes.fr/hal-01483473

M. Avellaneda and F. Lin, Compactness methods in the theory of homogenization, Communications on Pure and Applied Mathematics, vol.56, issue.6, pp.803-847, 1987.
DOI : 10.1002/cpa.3160400607

M. Avellaneda and F. Lin, Lp bounds on singular integrals in homogenization, Communications on Pure and Applied Mathematics, vol.43, issue.8-9, pp.8-9897, 1991.
DOI : 10.1002/cpa.3160440805

H. H. Bauschke and X. Wang, The kernel average for two convex functions and its application to the extension and representation of monotone operators, Transactions of the American Mathematical Society, vol.361, issue.11, pp.3615947-5965, 2009.
DOI : 10.1090/S0002-9947-09-04698-4

P. Bella and F. Otto, Corrector Estimates for Elliptic Systems with Random Periodic Coefficients, Multiscale Modeling & Simulation, vol.14, issue.4
DOI : 10.1137/15M1037147
URL : http://arxiv.org/abs/1409.5271

J. Ben-artzi, D. Marahrens, and S. Neukamm, Moment bounds on the corrector of stochastic homogenization of non-symmetric elliptic finite difference equations, Communications in Partial Differential Equations, vol.140, issue.2
DOI : 10.1007/s00440-004-0336-0

H. Brézis and I. Ekeland, Un principe variationnel associéassociéà certaineséquationscertaineséquations paraboliques. Le cas indépendant du temps, C. R. Acad. Sci. Paris Sér. A-B, vol.282, issue.17, pp.971-974, 1976.

J. G. Conlon and A. Naddaf, On Homogenization Of Elliptic Equations With Random Coefficients, Electronic Journal of Probability, vol.5, issue.0, p.pp, 2000.
DOI : 10.1214/EJP.v5-65

G. , D. Maso, and L. Modica, Nonlinear stochastic homogenization, Ann. Mat. Pura Appl, vol.144, issue.4, pp.347-389, 1986.

G. , D. Maso, and L. Modica, Nonlinear stochastic homogenization and ergodic theory, J. Reine Angew. Math, vol.368, pp.28-42, 1986.

I. Ekeland and R. Temam, Convex analysis and variational problems, Translated from the French, Studies in Mathematics and its Applications, 1976.
DOI : 10.1137/1.9781611971088

S. Fitzpatrick, Representing monotone operators by convex functions, Miniconference on Functional Analysis and Optimization, pp.59-65, 1988.

J. Geng and Z. Shen, The Neumann problem and Helmholtz decomposition in convex domains, Journal of Functional Analysis, vol.259, issue.8, pp.2147-2164, 2010.
DOI : 10.1016/j.jfa.2010.07.005

N. Ghoussoub, Self-dual partial differential systems and their variational principles, 2009.

N. Ghoussoub, A. Moameni, and R. Z. Sáiz, Abstract, Advanced Nonlinear Studies, vol.11, issue.2, pp.323-360, 2011.
DOI : 10.1515/ans-2011-0206

M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals, Acta Mathematica, vol.148, issue.0, pp.31-46, 1982.
DOI : 10.1007/BF02392725

M. Giaquinta and G. Modica, Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math, vol.311312, pp.145-169, 1979.

. Giusti, Direct methods in the calculus of variations, 2003.
DOI : 10.1142/5002

A. Gloria and D. Marahrens, Annealed estimates on the Green functions and uncertainty quantification, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.33, issue.5
DOI : 10.1016/j.anihpc.2015.04.001
URL : https://hal.archives-ouvertes.fr/hal-01093386

A. Gloria, S. Neukamm, and F. Otto, An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.2, pp.325-346, 2014.
DOI : 10.1051/m2an/2013110
URL : https://hal.archives-ouvertes.fr/hal-00863488

A. Gloria, S. Neukamm, and F. Otto, Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics, Inventiones mathematicae, vol.27, issue.4, pp.455-515, 2015.
DOI : 10.1007/s00222-014-0518-z
URL : https://hal.archives-ouvertes.fr/hal-01093405

A. Gloria, S. Neukamm, and F. Otto, A regularity theory for random elliptic operators, pp.1409-2678
URL : https://hal.archives-ouvertes.fr/hal-01093368

A. Gloria and F. Otto, An optimal variance estimate in stochastic homogenization of discrete elliptic equations, The Annals of Probability, vol.39, issue.3, pp.779-856, 2011.
DOI : 10.1214/10-AOP571
URL : https://hal.archives-ouvertes.fr/hal-00383953

A. Gloria and F. Otto, An optimal error estimate in stochastic homogenization of discrete elliptic equations, The Annals of Applied Probability, vol.22, issue.1, pp.1-28
DOI : 10.1214/10-AAP745
URL : https://hal.archives-ouvertes.fr/inria-00457020

A. Gloria and F. Otto, Quantitative results on the corrector equation in stochastic homogenization
URL : https://hal.archives-ouvertes.fr/hal-01093381

C. Kenig, F. Lin, and Z. Shen, Convergence Rates in L 2 for Elliptic Homogenization Problems, Archive for Rational Mechanics and Analysis, vol.75, issue.1, pp.1009-1036, 2012.
DOI : 10.1007/s00205-011-0469-0
URL : http://arxiv.org/abs/1103.0023

C. Kenig, F. Lin, and Z. Shen, Homogenization of elliptic systems with Neumann boundary conditions, Journal of the American Mathematical Society, vol.26, issue.4, pp.901-937, 2013.
DOI : 10.1090/S0894-0347-2013-00769-9

A. Lamacz, S. Neukamm, and F. Otto, Moment bounds for the corrector in stochastic homogenization of a percolation model, Electronic Journal of Probability, vol.20, issue.0
DOI : 10.1214/EJP.v20-3618

D. Marahrens and F. Otto, Annealed estimates on the Green's function, pp.1304-4408
DOI : 10.1007/s00440-014-0598-0
URL : http://arxiv.org/abs/1304.4408

J. Mourrat, Variance decay for functionals of the environment viewed by the particle, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.1, pp.294-327, 2011.
DOI : 10.1214/10-AIHP375
URL : https://hal.archives-ouvertes.fr/hal-01271688

A. Naddaf and T. Spencer, Estimates on the variance of some homogenization problems, 1998.

B. Nayroles, Deux théorèmes de minimum pour certains systèmes dissipatifs, C. R. Acad. Sci. Paris Sér. A-B, vol.282, issue.17, pp.1035-1038, 1976.

J. Nolen, Normal approximation for a random elliptic equation. Probab. Theory Related Fields, p.2014
DOI : 10.1007/s00440-013-0517-9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.2012

J. Penot, The relevance of convex analysis for the study of monotonicity, Nonlinear Analysis, vol.58, issue.7-8, pp.855-871, 2004.
DOI : 10.1016/j.na.2004.05.018

R. T. Rockafellar and R. J. Wets, Variational analysis, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1998.
DOI : 10.1007/978-3-642-02431-3

A. Visintin, Scale-transformations and homogenization of maximal monotone relations with applications, Asymptot. Anal, vol.82, issue.3-4, pp.233-270, 2013.

A. Visintin, Variational formulation and structural stability of monotone equations, Calculus of Variations and Partial Differential Equations, vol.IV, issue.2, pp.273-317, 2013.
DOI : 10.1007/s00526-012-0519-y