  Several experiments reveal the inhomogeneous character of the superconducting
state that occurs when the carrier density of the two-dimensional electron gas
formed at the LaXO3/SrTiO3 (X=Al or Ti) interface is tuned above a threshold
value by means of gating. Re-analyzing previous measurements, that highlight
the presence of two kinds of carriers, with low and high mobility, we shall
provide a description of multi-carrier magneto-transport in an inhomogeneous
two-dimensional electron gas, gaining insight into the properties of the
physics of the systems under investigation. We shall then show that the
measured resistance, superfluid density, and tunneling spectra result from the
percolative connection of superconducting "puddles" with randomly distributed
critical temperatures, embedded in a weakly localizing metallic matrix. We
shall also show that this scenario is consistent with the characteristics of
the superconductor-to-metal transition driven by a magnetic field. A
multi-carrier description of the superconducting state, within a weak-coupling
BCS-like model, will be finally discussed.
