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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
DOI: 10.2140/memocs.2013.1.233
Abstract

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
Mathematical Subject Classification 2010
Primary: 35P05, 47A10, 74K20
Milestones
Received: 7 March 2012
Revised: 21 July 2012
Accepted: 28 August 2012
Published: 26 August 2013

Communicated by Francesco dell'Isola
Authors
Fedor L. Bakharev
Mathematics and Mechanics Faculty
St. Petersburg State University
198904 St. Petersburg
Russia
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