On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems

This paper concerns periodic multiscale homogenization for fully nonlinear equations of the form u(epsilon) + H(epsilon) (x, x/epsilon, ..., x/epsilon(h), Du(epsilon), D(2)u(epsilon)) = 0. The operators H(epsilon) are a regular perturbations of some uniformly elliptic, convex operator H(epsilon). As epsilon goes to 0, the solutions u(epsilon) converge locally uniformly to the solution u of a suitably defined effective problem. The purpose of this paper is to obtain an estimate of the corresponding rate of convergence. Finally, some examples are discussed.