The Annals of Probability
- Ann. Probab.
- Volume 42, Number 3 (2014), 865-905.
The obstacle problem for quasilinear stochastic PDEs: Analytical approach
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.
Ann. Probab., Volume 42, Number 3 (2014), 865-905.
First available in Project Euclid: 26 March 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 31B150
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