Two-phase anisotropic free boundary problems and applications to the   Bellman equation in 2D
  We prove Lipschitz continuity of solutions to a class of rather general two-phase anisotropic free boundary problems in 2D and we classify global solutions. As a consequence, we obtain $C^{2,1}$ regularity of solutions to the Bellman equation in 2D. 
Luis Caffarelli, Daniela De Silva, Ovidiu Savin
math.AP