Abstract

In general, superbiharmonic functions do not satisfy a minimum principle like superharmonic functions do, i.e., functions u with 0≢Δ²u ≥ 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.

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