On Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients
arXiv:1904.10121
Abstract
The global equi-continuity estimate on Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of Lp-viscosity solutions is established via an approximation of given data. The local Hölder continuity estimate on the first derivative of Lp-viscosity solutions is shown when the obstacles belong to C^{1,β}, and p>n.