Floquet-Bloch Theory for Elliptic Problems with Discontinuous Coefficients

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 9783764399931. (The full text of this publication is not available from this repository)

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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
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 > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 04 Oct 2012 10:07
Last Modified: 28 Jul 2014 08:08
Resource URI: http://kar.kent.ac.uk/id/eprint/31247 (The current URI for this page, for reference purposes)
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