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We systematically develop a density functional description for theequilibrium properties of a two-dimensional, harmonically trapped,spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizs\"ackerapproximation. We pay particular attention to the construction of thetwo-dimensional kinetic energy functional, where corrections beyond the localdensity approximation must be motivated with care. We also present an intuitivederivation of the interaction energy functional associated with the dipolarinteractions, and provide physical insight into why it can be represented as alocal functional. Finally, a simple, and highly efficient self-consistentnumerical procedure is developed to determine the equilibrium density of thesystem for a range of dipole interaction strengths.

Thomas-Fermi von Weizs\"acker theory for a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas