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2013-17

In any dimension a ``clamped plate´´ with a uniform weight may change sign

by Hans-Christoph Grunau, Guido Sweers.


Series: 2013-17, Preprints

MSC:
35J40 Boundary value problems for higher-order elliptic equations

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 $Omega$ such that even the
solution of $Delta^2 u=1$ in $Omega$ with the homogeneous Dirichlet
boundary conditions $u=u_nu=0$ on $partialOmega$ is sign-changing.
In two dimensions this corresponds to the Kirchhoff-Love model of a
clamped plate with a uniform weight.

Keywords:
clamped plate equation, uniform load, sign changing solution