## Abstract

We study the asymptotic behavior of the spectrum of an elliptic operator with periodically oscillating coefficients, in a thin domain, with vanishing Dirichlet conditions. Two cases are treated: the case where the periodicity of the oscillations and the thickness of the domain have the same order of magnitude and the case where the oscillations have a frequency much greater than the thickness of the domain. A physical motivation can be to understand the behavior of the probability density associated to the wave function of a particle confined to a very thin domain, with periodically varying characteristics. To cite this article: R. Ferreira, M.L. Mascarenhas, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original language | English (US) |
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Pages (from-to) | 579-584 |

Number of pages | 6 |

Journal | Comptes Rendus Mathematique |

Volume | 346 |

Issue number | 9-10 |

DOIs | |

State | Published - May 2008 |

Externally published | Yes |

### Bibliographical note

Funding Information:This research was supported by POCI/MAT/60587/2004, by FCT-Plurianual (CMA) and by SFRH/BD/25573/2005. The authors thank M. Bendsœ for suggesting the problem, D. Krejcˇirík and D. Borisov for having pointed out some references, and CMAF for the hospitality.

## ASJC Scopus subject areas

- Mathematics(all)