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The obstacle problem for quasilinear stochastic PDEs with degenerate operator

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  • Yang, Xue
  • Zhang, Jing

Abstract

We prove the existence and uniqueness of solution of quasilinear stochastic partial differential equations with obstacle (OSPDEs in short) in degenerate case. Using De Giorgi’s iteration, we deduce the Lp-estimates for the time–space uniform norm of weak solutions.

Suggested Citation

  • Yang, Xue & Zhang, Jing, 2019. "The obstacle problem for quasilinear stochastic PDEs with degenerate operator," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3055-3079.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:9:p:3055-3079
    DOI: 10.1016/j.spa.2018.08.009
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    References listed on IDEAS

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    1. Xu, Tiange & Zhang, Tusheng, 2009. "White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3453-3470, October.
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    Cited by:

    1. Liu, Ruoyang & Tang, Shanjian, 2024. "The obstacle problem for stochastic porous media equations," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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