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The global equi-continuity estimate on $L^p$-viscosity solutions of parabolicbilateral obstacle problems with unbounded ingredients is established whenobstacles are merely continuous. The existence of $L^p$-viscosity solutions isestablished via an approximation of given data. The local H\"older continuityestimate on the space derivative of $L^p$-viscosity solutions is shown when theobstacles belong to $C^{1, \beta}$, and $p>n+2$.

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