Higher order convergence rates in the homogenization of non-divergence form equations on perforated domains with oblique boundary conditions

We establish higher order convergence rates for the homogenization of second order elliptic equations in non-divergence form, posed on periodically perforated domains with oblique boundary conditions on the perforation boundaries. Under a compatibility condition that ensures the solvability of the associated cell problems, we construct explicit families of interior and boundary correctors of arbitrary order. These correctors yield a rigorous asymptotic expansion of the solution $ u^ \varepsilon $, from which we derive the quantitative estimates for the higher order convergence rates. In particular, we obtain an estimate for the rate of convergence of $ u^ \varepsilon $ to the solution $ \overline{u} $ of the homogenized problem.