Positivity for the clamped plate under tension

Sascha Eichmann (Tuebingen)

Abstract:
We examine a clamped thin plate under an external force and ask ourself under which 
circumstances an upward force, i.e. upwards pushing, yields upwards bending.

Here we examine a model by Bickley, which employs the bilaplacian and some lower order terms. 
These lower order terms are connected to the tension of the thin plate.
It then turns out, that if this tension is big enough in dependence of the applied force, 
we indeed have upwards bending.

We will discuss the main ideas of the proof, an application to shape optimization in 
which we look for an 'optimal' domain for positivity preserving and some open questions.

This is joint work with Reiner Schätzle.