@article{1014,
  abstract     = {We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the regularity at the boundary: We consider problems posed on the half-space with homogeneous Dirichlet boundary conditions and derive an associated C1,α-type large-scale regularity theory in the form of a corresponding decay estimate for the homogenization-adapted tilt-excess. This regularity theory entails an associated Liouville-type theorem. The results are based on the existence of homogenization correctors adapted to the half-space setting, which we construct-by an entirely deterministic argument-as a modification of the homogenization corrector on the whole space. This adaption procedure is carried out inductively on larger scales, crucially relying on the regularity theory already established on smaller scales.},
  author       = {Fischer, Julian L and Raithel, Claudia},
  issn         = {00361410},
  journal      = {SIAM Journal on Mathematical Analysis},
  number       = {1},
  pages        = {82 -- 114},
  publisher    = {Society for Industrial and Applied Mathematics },
  title        = {{Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space}},
  doi          = {10.1137/16M1070384},
  volume       = {49},
  year         = {2017},
}