Examples of periodic elastic waveguides are constructed, the essential spectrum of which has a gap, i.e. an open interval in the positive real semiaxis intersecting with the discrete spectrum only. The gap is detected with the help of an inequality of Korn's type and the max-min principle for eigenvalues of self-adjoint positive operators. Under a certain symmetry assumption, it is demonstrated that the first band of the essential spectrum can include eigenvalues in the point spectrum. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Gaps in the essential spectrum of periodic elastic waveguides / Cardone, G; Minutolo, V; Nazarov, Sa. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK. - ISSN 0044-2267. - 89:9(2009), pp. 729-741. [10.1002/zamm.200800221]
Gaps in the essential spectrum of periodic elastic waveguides
Cardone G
;
2009
Abstract
Examples of periodic elastic waveguides are constructed, the essential spectrum of which has a gap, i.e. an open interval in the positive real semiaxis intersecting with the discrete spectrum only. The gap is detected with the help of an inequality of Korn's type and the max-min principle for eigenvalues of self-adjoint positive operators. Under a certain symmetry assumption, it is demonstrated that the first band of the essential spectrum can include eigenvalues in the point spectrum. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim| File | Dimensione | Formato | |
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