## Abstract

In the homogenization of second order elliptic equations with periodic coefficients, it is well known that the rate of convergence of the zero order corrector u_{n} - u^{hom} in the L^{2} norm is 1/n, the same as the scale of periodicity (see Jikov et al [6]). It is possible to have the same rate of convergence in the case of almost periodic coefficients under some stringent structural conditions on the coefficients (see Kozlov [7]). The goal of this note is to construct almost periodic media where the rate of convergence is lower than 1/n. To that aim, in the one dimensional setting, we introduce a family of random almost periodic coefficients for which we compute, using Fourier series analysis, the mean rate of convergence r_{n} (mean with respect to the random parameter). This allows us to present examples where we find r_{n} ≫ 1/n^{r} for every r > 0, showing a big contrast with the random case considered by Bourgeat and Piatnitski [2] where r_{n} ∼ 1/√n.

Original language | English |
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Pages (from-to) | 503-514 |

Number of pages | 12 |

Journal | Discrete And Continuous Dynamical Systems |

Volume | 13 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jul 2005 |

## Keywords

- Correctors
- Fourier analysis
- Homogenization
- Irrationality measure
- Random almost periodic coefficients
- Rate of convergence