  We study the end stages of gravitational collapse of the thin shell of matter
in ingoing Eddington-Finkelstein coordinates. We use the functional Schrodinger
formalism to capture quantum effects in the near singularity limit. We find
that that the equations of motion which govern the behavior of the collapsing
shell near the classical singularity become strongly non-local. This reinforces
previous arguments that quantum gravity in the strong field regime might be
non-local. We managed to solve the non-local equation of motion for the dust
shell case, and found an explicit form of the wavefunction describing the
collapsing shell. This wavefunction and the corresponding probability density
are non-singular at the origin, thus indicating that quantization should be
able to rid gravity of singularities, just as it was the case with the singular
Coulomb potential.
