  We show that the Kohn-Sham positive-definite kinetic energy (KE) density
significantly differs from the von Weizs\"acker (VW) one at the nuclear cusp as
well as in the asymptotic region. At the nuclear cusp, the VW functional is
shown to be linear and the contribution of p-type orbitals to the KE density is
theoretically derived and numerically demonstrated in the limit of infinite
nuclear charge, as well in the semiclassical limit of neutral large atoms. In
the latter case, it reaches 12 of the KE density. In the asymptotic region we
find new exact constraints for meta Generalized Gradient Approximation
(meta-GGA) exchange functionals: with an exchange enhancement factor
proportional to $\sqrt{\alpha}$, where $\alpha$ is the common meta-GGA
ingredient, both the exchange energy density and the potential are proportional
to the exact ones. In addition, this describes exactly the large-gradient limit
of quasi-two dimensional systems.
