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

Shota Tateyama

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

Analysis of PDEs 2020-01-28 v1

Authors: Shota Tateyama

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 $p>n+2$ .

Keywords

l^p-viscosity solutions parabolic bilateral obstacle problems unbounded ingredients equi-continuity holder continuity

Cite

@article{arxiv.2001.09582,
  title  = {On $L^p$-viscosity solutions of parabolic bilateral obstacle problems with unbounded ingredients},
  author = {Shota Tateyama},
  journal= {arXiv preprint arXiv:2001.09582},
  year   = {2020}
}

Comments

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

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