A sufficient condition for a discrete spectrum of the Kirchhoff plate   with an infinite peak
  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. 
F. L. Bakharev and S. A. Nazarov and G. H. Sweers
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