We study the ground state properties of the 1‐D boson and fermion Hubbard models in harmonic traps with an underlying lattice. The physics of these systems is found to be fundamentally different from the homogeneous case. Global quantities lose their meaning and Mott domains appear for a continuous range of incommensurate fillings. A local order parameter is defined to characterize the Mott insulating phases that coexist with the metallic ones. Finally, the phase diagrams show richer structures than in the homogeneous models. © 2003 American Institute of Physics