On a weak solution of Einstein equations for expanding dust
  An expanding spherically symmetric dust cloud is considered in a framework of
general relativity. Initial conditions leading to a shell-crossing singularity
are chosen. The way to construct a weak solution for such a case is proposed.
Suggested method consists in cutting off the region containing the
shell-crossing and matching the remaining parts of space-time at a thin shell.
Junction conditions determine the motion of that thin shell. The singular part
of dust stress-energy tensor is nontrivial only after the shell-crossing
occurs. Before that the solution coincides with Lemaitre - Tolman - Bondi one.
A toy model representing an underdensed region in Universe is discussed.
