---
res:
  bibo_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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Julian L
      foaf_name: Fischer, Julian L
      foaf_surname: Fischer
      foaf_workInfoHomepage: http://www.librecat.org/personId=2C12A0B0-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-0479-558X
  - foaf_Person:
      foaf_givenName: Stefan
      foaf_name: Neukamm, Stefan
      foaf_surname: Neukamm
  bibo_doi: 10.1007/s00205-021-01686-9
  bibo_issue: '1'
  bibo_volume: 242
  dct_date: 2021^xs_gYear
  dct_identifier:
  - UT:000668431200001
  dct_isPartOf:
  - http://id.crossref.org/issn/0003-9527
  - http://id.crossref.org/issn/1432-0673
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_subject:
  - Mechanical Engineering
  - Mathematics (miscellaneous)
  - Analysis
  dct_title: Optimal homogenization rates in stochastic homogenization of nonlinear
    uniformly elliptic equations and systems@
...