L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, 2000.

M. Avellaneda and F. H. Lin, Compactness methods in the theory of homogenization, Communications on Pure and Applied Mathematics, vol.56, issue.6, pp.803-847, 1987.
DOI : 10.1007/978-3-642-96379-7

M. Avellaneda and F. H. Lin, Compactness methods in the theory of homogenization II: Equations in non-divergence form, Communications on Pure and Applied Mathematics, vol.37, issue.2, pp.139-172, 1989.
DOI : 10.1007/978-3-642-96379-7

M. Avellaneda and F. H. Lin, Lp bounds on singular integrals in homogenization, Communications on Pure and Applied Mathematics, vol.43, issue.8-9, pp.897-910, 1991.
DOI : 10.1002/cpa.3160440805

A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic analysis for periodic structures, Studies in Mathematics and its Applications, 1978.
DOI : 10.1090/chel/374

X. Blanc, M. Josien, and C. , Le Bris, Local approximation of the gradient for multiscale problems with defects

X. Blanc, C. Le-bris, and P. Lions, A Possible Homogenization Approach for the Numerical Simulation of Periodic Microstructures with Defects, Milan Journal of Mathematics, vol.88, issue.2, pp.351-367, 2012.
DOI : 10.4171/ZAA/1133

X. Blanc, C. Le-bris, and P. Lions, Profils locaux etprobì emes elliptiquesà elliptiquesà plusieurséchellesplusieurséchelles avec défauts, [Local profiles and elliptic problems at different scales with defects] Note aux Comptes Rendus de l'Académie des Sciences, pp.203-208, 2015.
DOI : 10.1016/j.crma.2015.01.003

X. Blanc, C. Le-bris, and P. Lions, Local Profiles for Elliptic Problems at Different Scales: Defects in, and Interfaces between Periodic Structures, Communications in Partial Differential Equations, vol.26, issue.12, pp.2173-2236, 2015.
DOI : 10.1007/978-1-4612-1015-3

URL : https://hal.archives-ouvertes.fr/hal-01143193

X. Blanc, C. Le-bris, and P. Lions, On correctors for linear elliptic homogenization in the presence of local defects: the case of advection-diffusion
URL : https://hal.archives-ouvertes.fr/hal-01697105

X. Blanc, F. Legoll, and A. Anantharaman, Asymptotic behaviour of Green functions of divergence form operators with periodic coefficients, Applied Mathematics Research Express, issue.1, pp.79-101, 2013.

V. I. Bogachev and S. V. Shaposhnikov, Integrability and continuity of solutions to double divergence form equations, Annali di Matematica Pura ed Applicata (1923 -), vol.254, issue.10, pp.1609-1635, 2017.
DOI : 10.1007/978-1-4612-1015-3

V. I. Bogachev, N. V. Krylov, M. Röckner, and S. V. Shaposhnikov, Fokker- Planck-Kolmogorov equations, Mathematical Surveys and Monographs, vol.207, 2015.
DOI : 10.1090/surv/207

H. O. Cordes, Zero order a priori estimates for solutions of elliptic differential equations, Proc. Sympos. Pure Math, pp.157-166, 1961.
DOI : 10.1090/pspum/004/0146511

G. Dolzmann and S. Müller, Estimates for Green's matrices of elliptic systems byL p theory, Manuscripta Mathematica, vol.17, issue.1, pp.261-273, 1995.
DOI : 10.1007/BF02567822

B. Engquist and P. Souganidis, Asymptotic and numerical homogenization, Acta Numer, pp.147-190, 2008.
DOI : 10.1017/s0962492906360011

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, 1983.

M. Giaquinta and L. Martinazzi, An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs, Lecture Notes Scuola Normale Superiore di Pisa, 2012.

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order. Reprint of the 1998 edition, Classics in Mathematics, 2001.

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

M. Grüter and K. O. Widman, The Green function for uniformly elliptic equations, Manuscripta Mathematica, vol.26, issue.3, pp.303-342, 1982.
DOI : 10.1007/BF01166225

V. V. Jikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of differential operators and integral functionals, 1994.
DOI : 10.1007/978-3-642-84659-5

C. Kenig and W. M. Ni, On the elliptic equation Lu ? k + K exp, Ann. Scuola Norm. Super. Pisa (IV), vol.2, issue.12, pp.191-224, 1985.

C. Kenig, F. H. Lin, and Z. Shen, Periodic Homogenization of Green and Neumann Functions, Communications on Pure and Applied Mathematics, vol.59, issue.3, pp.1219-1262, 2014.
DOI : 10.1016/0022-1236(84)90066-1

P. Lions, The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.1, issue.4, pp.109-145, 1984.
DOI : 10.1016/S0294-1449(16)30422-X

Y. Meyer, Ondelettes et opérateurs. II. [Wavelets and operators. II] Opérateurs de Caldern-Zygmund

J. Moser, On Harnack's theorem for elliptic differential equations, Communications on Pure and Applied Mathematics, vol.13, issue.3, pp.577-591, 1961.
DOI : 10.1007/978-3-642-47434-7

E. M. Stein, Harmonic analysis: real-variable methods, orthogonality , and oscillatory integrals. Princeton Mathematical Series, 43. Monographs in Harmonic Analysis, III, 1993.