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A sufficient
condition for a discrete spectrum of the Kirchhoff plate with
an infinite peak
Fedor L. Bakharev, Sergey A. Nazarov and Guido H. Sweers
Vol. 1 (2013), No. 2, 233–247
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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. |
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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Authors |
| Fedor L. Bakharev | |
| Mathematics and Mechanics
Faculty St. Petersburg State University 198904 St. Petersburg Russia |
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| Sergey A. Nazarov | |
| Institute of Problems of Mechanical
Engineering Russian Academy of Sciences 199178 St. Petersburg Russia |
Mathematics and Mechanics
Faculty St. Petersburg State University Universitetsky pr., 28 198504, Stary Peterhof Russia |
| Guido H. Sweers | |
| Mathematisches Institut Universität zu Köln D-50931 Cologne Germany |
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