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 -> 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.
On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems
CAMILLI, FABIO;
2011-01-01
Abstract
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 -> 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.File in questo prodotto:
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