The Annals of Probability

The obstacle problem for quasilinear stochastic PDEs: Analytical approach

Laurent Denis, Anis Matoussi, and 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.

Article information

Source
Ann. Probab. Volume 42, Number 3 (2014), 865-905.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1395838118

Digital Object Identifier
doi:10.1214/12-AOP805

Mathematical Reviews number (MathSciNet)
MR3189060

Zentralblatt MATH identifier
1298.60064

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 31B150

Keywords
Parabolic potential regular measure stochastic partial differential equations obstacle problem penalization method Itô’s formula comparison theorem space–time white noise

Citation

Denis, Laurent; Matoussi, Anis; Zhang, Jing. The obstacle problem for quasilinear stochastic PDEs: Analytical approach. Ann. Probab. 42 (2014), no. 3, 865--905. doi:10.1214/12-AOP805. https://projecteuclid.org/euclid.aop/1395838118


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