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

Abstract

The global equi-continuity estimate on $L^p$-viscosity solutions of parabolic 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 H\"older continuity estimate on the space derivative of $L^p$-viscosity solutions is shown when the obstacles belong to $C^{1, \beta}$, and $p>n+2$.