## Abstract

Pointwise estimate for the solutions of elliptic equations in periodic perforated domains is concerned. Let ε denote the size ratio of the period of a periodic perforated domain to the whole domain. It is known that even if the given functions of the elliptic equations are bounded uniformly in ε, the C^{1,α} norm and the W^{2,p} norm of the elliptic solutions may not be bounded uniformly in ε. It is also known that when ε closes to 0, the elliptic solutions in the periodic perforated domains approach a solution of some homogenized elliptic equation. In this work, the Hölder uniform bound in ε and the Lipschitz uniform bound in ε for the elliptic solutions in perforated domains are proved. The L^{∞} and the Lipschitz convergence estimates for the difference between the elliptic solutions in the perforated domains and the solution of the homogenized elliptic equation are derived.

Original language | English |
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Pages (from-to) | 1961-1986 |

Number of pages | 26 |

Journal | Communications on Pure and Applied Analysis |

Volume | 14 |

Issue number | 5 |

DOIs | |

State | Published - 1 Sep 2015 |

## Keywords

- Homogenized elliptic equation
- Periodic perforated domains
- Two-phase media