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arXiv · 1202.3296

The obstacle problem for quasilinear stochastic PDEs: Analytical approach

Laurent Denis·Anis Matoussi·Jing Zhang
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Abstract

We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (OSPDE in short). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair $(u,\nu)$ where $u$ is a predictable continuous process which takes values in a proper Sobolev space and $\nu$ is a random regular measure satisfying the minimal Skohorod condition.

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Laurent Denis, Anis Matoussi, Jing Zhang. 2012-02-15. The obstacle problem for quasilinear stochastic PDEs: Analytical approach. https://doi.org/10.1214/12-aop805

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