Optimal regularity at the free boundary for the infinity obstacle   problem
  This paper deals with the obstacle problem for the infinity Laplacian. The main results are a characterization of the solution through comparison with cones that lie above the obstacle and the sharp $C^{1,1/3}$--regularity at the free boundary. 
Julio D. Rossi, Eduardo V. Teixeira and Jos\'e Miguel Urbano
math.AP