### Abstract

Let Ω_{0} be a domain in the cube (0, 2π)^{n}, and let χ_{τ}(x) be a function that equals 1 inside Ω_{0}, equals τ in (0, 2π)^{n}/Ω_{0}, and that is extended periodically to R^{n}. It is known that, in the limit τ → ∞, the spectrum of the operator - ∇χ_{τ}(x)∇ exhibits the band-gap structure. We establish the asymptotic behavior of the density of states function in the bands.

Original language | English (US) |
---|---|

Pages (from-to) | 355-380 |

Number of pages | 26 |

Journal | Communications in Partial Differential Equations |

Volume | 27 |

Issue number | 1-2 |

DOIs | |

State | Published - 2002 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics

### Cite this

**On the density of states of periodic media in the large coupling limit.** / Friedlander, Leonid.

Research output: Contribution to journal › Article

*Communications in Partial Differential Equations*, vol. 27, no. 1-2, pp. 355-380. https://doi.org/10.1081/PDE-120002790

}

TY - JOUR

T1 - On the density of states of periodic media in the large coupling limit

AU - Friedlander, Leonid

PY - 2002

Y1 - 2002

N2 - Let Ω0 be a domain in the cube (0, 2π)n, and let χτ(x) be a function that equals 1 inside Ω0, equals τ in (0, 2π)n/Ω0, and that is extended periodically to Rn. It is known that, in the limit τ → ∞, the spectrum of the operator - ∇χτ(x)∇ exhibits the band-gap structure. We establish the asymptotic behavior of the density of states function in the bands.

AB - Let Ω0 be a domain in the cube (0, 2π)n, and let χτ(x) be a function that equals 1 inside Ω0, equals τ in (0, 2π)n/Ω0, and that is extended periodically to Rn. It is known that, in the limit τ → ∞, the spectrum of the operator - ∇χτ(x)∇ exhibits the band-gap structure. We establish the asymptotic behavior of the density of states function in the bands.

UR - http://www.scopus.com/inward/record.url?scp=0036381857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036381857&partnerID=8YFLogxK

U2 - 10.1081/PDE-120002790

DO - 10.1081/PDE-120002790

M3 - Article

AN - SCOPUS:0036381857

VL - 27

SP - 355

EP - 380

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 1-2

ER -