Particle density and non-local kinetic energy density functional for two-dimensional harmonically confined Fermi vapors

We evaluate analytically some ground state properties of two-dimensional ha rmonically confined Fermi vapors with isotropy and for an arbitrary number of closed shells. We first derive a differential form of the virial theorem and an expression for the kinetic energy density in terms of the fermion p article density and its low-order derivatives. These results allow an expli cit differential equation to be obtained for the particle density. The equa tion is third-order, linear and homogeneous. We also obtain a relation betw een the turning points of kinetic energy and particle densities, and an exp ression of the non-local kinetic energy density functional.