A clamped plate with a uniform weight may change sign

@article{Grunau2014ACP,
  title={A clamped plate with a uniform weight may change sign},
  author={Hans-Christoph Grunau and Guido Sweers},
  journal={Discrete and Continuous Dynamical Systems - Series S},
  year={2014},
  volume={7},
  pages={761-766}
}
  • H. Grunau, G. Sweers
  • Published 2014
  • Mathematics
  • Discrete and Continuous Dynamical Systems - Series S
It is known that the Dirichlet bilaplace boundary value problem, which is used as a model for a clamped plate, is not sign preserving on general domains. It is also known that the corresponding first eigenfunction may change sign. In this note we will show that even a constant right hand side may result in a sign-changing solution. 
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In any dimension a “clamped plate” with a uniform weight may change sign
Abstract Positivity preserving properties have been conjectured for the bilaplace Dirichlet problem in many versions. In this note we show that in any dimension there exist bounded smooth domains ΩExpand
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