Submitted to: AstrophysicalJournal

In this paper, we extend the calculations conducted previously in the stellar regime (Chabrier, 2001) to determine the brown dwarf initial mass function in the Galactic disk. We perform Monte Carlo calculations taking into account the brown dwarf formation rate, spatial distribution and binary fraction. Comparison with existing surveys seems to exclude a power-law mass function as steep as the one determined in the stellar regime below 1 M⊙, i.e. dn/dm ∝ m, and tends to favor a more flatish behaviour. Although a power-law mass function in the substellar regime can not be excluded by present day observational constraints, a form dn/dm ∝ m, i.e. dn/d logm = constant, seems to be an upper limit. Comparison with methane-dwarf detections tends to favor an eventually decreasing form like the lognormal or the more general exponential distributions determined in the previous paper. We calculate predicting brown dwarf counts in near-infrared color diagrams and brown dwarf discovery functions for various types of mass functions and formation rates, and for different binary distributions. Based on these diagnostics, future large deep field surveys should be able to determine more precisely the brown dwarf mass function and to provide information about the formation of star-like objects stars and brown dwarfs along the Galactic history. These calculations yield the presently most accurate determination of the brown dwarf census in the Galactic disk. The brown dwarf number density is comparable to the stellar one, nBD ≃ n⋆ ≃ 0.1 pc , showing that the star formation process in the disk extends well into the substellar regime. The corresponding brown dwarf mass density, however, represents only about 10% of the stellar contribution, i.e. ρBD < ∼ 5.0 × 10 −3 M⊙pc . Adding up the local stellar density determined in the previous paper, we obtain the density of star-like objects, stars and brown