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

38 pages. arXiv admin note: substantial text overlap with arXiv:1904.10121

References in corpus (1)

• The double obstacle problem on non divergence form