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Abstract
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Sufficient conditions for a discrete spectrum of the biharmonic equation in a
two-dimensional peak-shaped domain are established. Different boundary conditions
from Kirchhoff’s plate theory are imposed on the boundary and the results depend
both on the type of boundary conditions and the sharpness exponent of the
peak.
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Keywords
Kirchhoff plate, cusp, peak, discrete and continuous
spectra
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Mathematical Subject Classification 2010
Primary: 35P05, 47A10, 74K20
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Milestones
Received: 7 March 2012
Revised: 21 July 2012
Accepted: 28 August 2012
Published: 26 August 2013
Communicated by Francesco dell'Isola
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