On $$L^p$$-viscosity solutions of bilateral obstacle problems with unbounded ingredients

Abstract

The global equi-continuity estimate on $$L^p$$ -viscosity solutions of bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of $$L^p$$ -viscosity solutions is established via an approximation of given data. The local Holder continuity estimate on the first derivative of $$L^p$$ -viscosity solutions is shown when the obstacles belong to $$C^{1,\beta }$$ , and $$p>n$$ .