Volume 48, Number 2, March-April 2014
Multiscale problems and techniques
Page(s) 325 - 346
Published online 21 January 2014
  1. G. Allaire and M. Amar, Boundary layer tails in periodic homogenization. ESAIM: COCV 4 (1999) 209–243. [CrossRef] [EDP Sciences] [Google Scholar]
  2. M. Avellaneda and F.-H. Lin, Compactness methods in the theory of homogenization. Commun. Pure Appl. Math. 40 (1987) 803–847. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Bourgeat and A. Piatnitski, Estimates in probability of the residual between the random and the homogenized solutions of one-dimensional second-order operator. Asymptotic Anal. 21 (1999) 303–315. [Google Scholar]
  4. J.G. Conlon and T. Spencer, Strong convergence to the homogenized limit of elliptic equations with random coefficients. Trans. AMS, in press. [Google Scholar]
  5. A. Gloria, Fluctuation of solutions to linear elliptic equations with noisy diffusion coefficients. Commun. Partial Differ. Eq. 38 (2013) 304–338. [CrossRef] [Google Scholar]
  6. A. Gloria, S. Neukamm, and F. Otto, Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics. MPI Preprint 91 (2013). [Google Scholar]
  7. A. Gloria, S. Neukamm and F. Otto, Approximation of effective coefficients by periodization in stochastic homogenization. In preparation. [Google Scholar]
  8. A. Gloria and F. Otto, Quantitative results on the corrector equation in stochastic homogenization of linear elliptic equations. In preparation. [Google Scholar]
  9. A. Gloria and F. Otto, An optimal variance estimate in stochastic homogenization of discrete elliptic equations. Ann. Probab. 39 (2011) 779–856. [CrossRef] [Google Scholar]
  10. A. Gloria and F. Otto, An optimal error estimate in stochastic homogenization of discrete elliptic equations. Ann. Appl. Probab. 22 (2012) 1–28. [CrossRef] [Google Scholar]
  11. R.J. Leveque, Finite difference methods for ordinary and partial differential equations. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2007). [Google Scholar]
  12. S.M. Kozlov, The averaging of random operators. Mat. Sb. (N.S.) 109 (1979) 188–202, 327. [MathSciNet] [Google Scholar]
  13. R. Künnemann, The diffusion limit for reversible jump processes on Zd with ergodic random bond conductivities. Commun. Math. Phys. 90 (1983) 27–68. [CrossRef] [Google Scholar]
  14. D. Marahrens and F. Otto, Annealed estimates on the Green’s function. MPI Preprint 69 (2012). [Google Scholar]
  15. S.J.N. Mosconi, Discrete regularity for elliptic equations on graphs. CVGMT. Available at (2001). [Google Scholar]
  16. A. Naddaf and T. Spencer, Estimates on the variance of some homogenization problems. Preprint (1998). [Google Scholar]
  17. H. Owhadi, Approximation of the effective conductivity of ergodic media by periodization. Probab. Theory Relat. Fields 125 (2003) 225–258. [CrossRef] [MathSciNet] [Google Scholar]
  18. G.C. Papanicolaou and S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients. In Random fields, Vol. I, II (Esztergom, 1979), vol. 27 of Colloq. Math. Soc. János Bolyai. North-Holland, Amsterdam (1981) 835–873. [Google Scholar]
  19. V.V. Yurinskiĭ, Averaging of symmetric diffusion in random medium. Sibirskii Matematicheskii Zhurnal 27 (1986) 167–180. [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you