Uniform estimates near the initial state for solutions to the two-phase   parabolic problem
  This paper is devoted to a proof of optimal regularity, near the initial state, for weak solutions to the two-phase parabolic obstacle problem. The approach used here is general enough to allow us to consider the initial data belonging to the class $C^{1,1}$. 
D.E. Apushkinskaya and N.N. Uraltseva
math.AP