Maximum principle for quasilinear stochastic PDEs with obstacle

Laurent Denis, Anis Matoussi, Jing Zhang
2014 Electronic Journal of Probability  
We prove a maximum principle for local solutions of quasilinear stochastic PDEs with obstacle (in short OSPDE). The proofs are based on a version of Itô's formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.
doi:10.1214/ejp.v19-2716 fatcat:vvoa5u3tmvgobl2y2qpgos2y7e