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;
2009-01-01
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, WeinheimFile in questo prodotto:
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