A priori estimates for the obstacle problem of Hessian type equations on   Riemannian manifolds
  We are concerned with a priori estimates for the obstacle problem of a wide class of fully nonlinear equations on Riemannian manifolds. We use new techniques introduced by Bo Guan and derive new results for a priori second order estimates of its singular perturbation problem under fairly general conditions. By approximation, the existence of a C^{1,1} viscosity solution is proved. 
Tingting Wang, WeiSong Dong, Gejun Bao
math.AP