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

by Hans-Christoph Grunau, Guido Sweers.

Series: 2013-17, Preprints

35J40 Boundary value problems for higher-order elliptic equations

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.

clamped plate equation, uniform load, sign changing solution