@article{10549,
abstract = {We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \varepsilon >0, we establish homogenization error estimates of the order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \varepsilon ^\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\alpha } regularity theory is available.},
author = {Fischer, Julian L and Neukamm, Stefan},
issn = {1432-0673},
journal = {Archive for Rational Mechanics and Analysis},
keywords = {Mechanical Engineering, Mathematics (miscellaneous), Analysis},
number = {1},
pages = {343--452},
publisher = {Springer Nature},
title = {{Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems}},
doi = {10.1007/s00205-021-01686-9},
volume = {242},
year = {2021},
}