We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a twodimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [PRA 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [PRB 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground state properties of strong long-range interacting bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.This manuscript is organized as follows. In Sec. II we introduce the Bose-Hubbard model and review the ground-state properties in the atomic limit, namely, when the kinetic energy is set to zero. In Section III we derive the mean-field Hamiltonian and employ the path-integral formalism to analytically determine the transition from incompressible to compressible phases. In Sec. IV we numerically determine the ground-state phase diagram and compare our results with the ones reported so far in the literature. The conclusions are drawn in Sec. V while the appendices provide details on the numerical methods for calculating the mean-field phase diagrams. arXiv:1902.05801v1 [cond-mat.quant-gas]