Positivity for the clamped plate equation under high tension

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