Weak solutions to mean curvature flow respecting obstacles I: the   graphical case
  We consider the problem of evolving hypersurfaces by mean curvature flow in the presence of obstacles, that is domains which the flow is not allowed to enter. In this paper, we treat the case of complete graphs and explain how the approach of M. Saez and the second author yields a global weak solution to the original problem for general initial data and onesided obstacles. 
Melanie Rupflin and Oliver C. Schn\"urer
math.DG math.AP