Georgia Institute of Technology College of Sciences

We discuss bilateral obstacle problems for fully nonlinear second order uniformly elliptic partial differential equations (PDE for short) with merely continuous obstacles. Obstacle problems arise not only in minimization of energy functionals under restriction by obstacles but also stopping time problems in stochastic optimal control theory. When the main PDE part is of divergence type, huge amount of works have been done. However, less is known when it is of non-divergence type. Recently, Duque showed that the Holder continuity of viscosity solutions of bilateral obstacle problems, whose PDE part is of non-divergence type, and obstacles are supposed to be Holder continuous. Our purpose is to extend his result to enable us to apply a much wider class of PDE. This is a joint work with Shota Tateyama (Tohoku University).