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arXiv 2001.095822020-01-27math.AP

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

Shota Tateyama

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

英文摘要：

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 $C^{1, β}$, and $p>n+2$.

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