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; Claudio, Marchi. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 6:1(2011), pp. 61-75. [10.3934/nhm.2011.6.61]

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

CAMILLI, FABIO;
2011

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.
2011
homogenization; rate of convergence; viscosity solutions
01 Pubblicazione su rivista::01a Articolo in rivista
On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems / Camilli, Fabio; Claudio, Marchi. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 6:1(2011), pp. 61-75. [10.3934/nhm.2011.6.61]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/357399
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