Mean curvature flow with obstacles: existence, uniqueness and regularity   of solutions
  We show short time existence and uniqueness of $\C^{1,1}$ solutions to the mean curvature flow with obstacles, when the obstacles are of class $\C^{1,1}$. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface. 
Gwenael Mercier (CMAP), Matteo Novaga
math.AP math.DG