by Hans-Christoph Grunau, Guido Sweers.
Series: 2013-17, Preprints
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