Two-scale cut-and-projection convergence for quasiperiodic monotone operators

Averaging a certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic structure in a higher dimensional space using the cut-and projection method. We characterize the cut-and-projection convergence limit of the nonlinear monotone partial differential operator -div sigma (x, Rx/eta, del u(eta)) for a bounded sequence u(eta) in W-0(1,p) (Omega)/ where 1 < p < infinity, and Omega is a bounded open subset in R-n with Lipschitz boundary. We identify the homogenized problem with a local equation defined on a hyperplane, or a lower dimensional plane in the higher-dimensional space. A new corrector result is established.