Brown, Brian Malcolm and Hoang, Vu and Plum, Michael and Wood, Ian
(2011)
*
Floquet-Bloch Theory for Elliptic Problems with Discontinuous Coefficients.
*
In: Janas, Jan and Kurasov, Pavel and Laptev, Ari and Naboko, Sergei and Stolz, Gunter, eds.
Spectral Theory and Analysis: Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2008.
Operator Theory: Advances and Applications
.
Springer, Poland, pp. 1-20.
ISBN 978-3-7643-9993-1.
(doi:10.1007/978-3-7643-9994-8_1)
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Official URL http://dx.doi.org/10.1007/978-3-7643-9994-8_1 |

## Abstract

We study spectral properties of elliptic problems of order 2m with periodic coefficients in L?. Our goal is to obtain a Floquet-Bloch type representation of the spectrum in terms of the spectra of associated operators acting on the period cell. Our approach using bilinear forms and operators in H?m-type spaces easily handles discontinuous coefficients and has the merit of being rather direct. In addition, the cell of periodicity is allowed to be unbounded, i.e. periodicity is not required in all spatial directions.

Item Type: | Book section |
---|---|

DOI/Identification number: | 10.1007/978-3-7643-9994-8_1 |

Uncontrolled keywords: | Floquet-Bloch, 2mth-order elliptic, spectral theory |

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Ian Wood |

Date Deposited: | 04 Oct 2012 10:07 UTC |

Last Modified: | 01 Aug 2019 10:35 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/31247 (The current URI for this page, for reference purposes) |

Wood, Ian: | https://orcid.org/0000-0001-7181-7075 |

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