TY - JOUR
AB - 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.
AU - Fischer, Julian L
AU - Neukamm, Stefan
ID - 10549
IS - 1
JF - Archive for Rational Mechanics and Analysis
KW - Mechanical Engineering
KW - Mathematics (miscellaneous)
KW - Analysis
SN - 0003-9527
TI - Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems
VL - 242
ER -