Nonexistence of Local Minima of Supersolutions for the Circular Clamped Plate

In general, superbiharmonic functions do not satisfy a minimum principle like superharmonic functions do, i.e., functions u with 0 ≡ ∆u ≥ 0 may have a strict local minimum in an interior point. We will prove, however, that when a superbiharmonic function is defined on a disk and additionally subject to Dirichlet boundary conditions, it cannot have interior local minima. For the linear model of the clamped plate this means that a circular plate, which is pushed from below, cannot bend downwards even locally.