## Abstract

We consider a Neumann problem for the Poisson equation in the periodically perforated Euclidean space. Each periodic perforation has a size proportional to a positive parameter ε. For each positive and small ε, we denote by v(ε,·) a suitably normalized solution. Then we are interested to analyze the behavior of v(ε,·) when ε is close to the degenerate value ε=0, where the holes collapse to points. In particular we prove that if n≥3, then v(ε,·) can be expanded into a convergent series expansion of powers of ε and that if n=2 then v(ε,·) can be expanded into a convergent double series expansion of powers of ε and εlogε. Our approach is based on potential theory and functional analysis and is alternative to those of asymptotic analysis.

Original language | English |
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Pages (from-to) | 253-272 |

Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |

Volume | 96 |

Issue number | 2 |

Early online date | 04 Mar 2015 |

DOIs | |

Publication status | Published - 01 Feb 2016 |

## Keywords

- Neumann problem
- Periodically perforated domain
- Real analytic continuation in Banach space
- Singularly perturbed domain