Nonexistence of local minima of supersolutions for the polyharmonic problems

In this note we study the nonexistence of local minima of the supersolutions of the polyharmonic equations on the balls under generalized homogeneous Dirichlet boundary conditions. Under suitable restriction on the dimensions, this means that a generalized clamped circular plate, which is pushed from below, cannot bend downwards even locally. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)