Positivity for the clamped plate equation under high tension

Abstract

In this article we consider positivity issues for the clamped plate equation with high tension γ > 0. This equation is given by ∆ 2 u − γ∆u = f under clamped boundary conditions. Here we show, that given a positive f , i.e. upwards pushing, we find a γ 0 > 0 such that for all γ ≥ γ 0 the bending u is indeed positive. This γ 0 only depends on the domain and the ratio of the L 1 and L ∞ norm of f . In contrast to a recent result by Cassani&Tarsia, our approach is valid in all dimensions.