## Abstract

We study the convergence rate of an asymptotic expansion for the elliptic and parabolic operators with rapidly oscillating coefficients. First we propose homogenized expansions which are convolution forms of Green function and given force term of elliptic equation. Then, using local L^{p}-theory, the growth rate of the perturbation of Green function is found. From the representation of elliptic solution by Green function, we estimate the convergence rate in L^{p} space of the homogenized expansions to the exact solution. Finally, we consider L^{2} (0, T : H^{1} (Ω)) or L^{∞}(Ω × (0, T)) convergence rate of the first order approximation for parabolic homogenization problems.

Original language | English |
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Pages (from-to) | 321-336 |

Number of pages | 16 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 287 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2003 Nov 15 |

### Bibliographical note

Funding Information:* Corresponding author. E-mail addresses: choe@yonsei.ac.kr (H.J. Choe), kibok@kaist.ac.kr (K.-B. Kong), colee@amath.kaist.ac.kr (C.-O. Lee). 1 Supported by KOSEF R01-2000-00008 and KRF.

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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