On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems
Fabio Camilli, ,Dip. di Matematica Pura e Applicata, Univ. dell'Aquila, loc. Monteluco di Roio, 67040 l'Aquila, Claudio Marchi · Networks and Heterogeneous Media · 2011
This paper concerns periodic multiscale homogenization for fully nonlinear equations of the form $u^\epsilon+H^\epsilon (x,\frac{x}{\epsilon},\ldots,\frac{x}{epsilon^k},Du^\epsilon,D^2u^\epsilon)=0$.The operators $H^\epsilon$ are a regular perturbations of some uniformly elliptic,convex operator $H$.As $\epsilon\to 0^+$, 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.