The in-plane and out-of-plane superconducting stiffness appear to vanish at
different transition temperatures, which contradicts thermodynamical
expectation. In addition, we observe a surprisingly strong dependence of the
out-of-plane stiffness transition on sample width. With evidence from Monte
Carlo simulations, this effect is explained by a crossover from three
dimensions into quasi one dimensional behavior of the finite sample. Due to an
essential singularity at the thermodynamic transition temperature Tc​, the
out-of-plane stiffness appears to vanish below Tc​ by an amount which is
proportional to the inverse width. A fit of our prediction to the data is used
to determine the value of the anisotropy parameter. Analogy to studies of
helium superfluids in nanopores is made