Nonexistence of local minima of supersolutions for the circular clamped plate

Hans-Christoph Grunau and Guido Sweers

Vol. 198 (2001), No. 2, 437–442

DOI: 10.2140/pjm.2001.198.437

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.

Milestones

Received: 5 August 1999

Published: 1 April 2001