The obstacle problem for quasilinear stochastic PDEs: Analytical approach

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.

Published in at http://dx.doi.org/10.1214/12-AOP805 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• The obstacle problem for quasilinear stochastic PDE's

Cited by in corpus (1)

• Theoretical analysis of a finite-volume scheme for a stochastic Allen-Cahn problem with constraint