The obstacle problem for quasilinear stochastic PDEs with degenerate operator

We prove the existence and uniqueness of solution of quasilinear stochastic partial differential equations with obstacle (OSPDEs in short) in degenerate case. Using De Giorgi's iteration, we de-duce the $L^p-$estimates for the time-space uniform norm of weak solutions.

[ 1 ] Denis L., Matoussi A. and Zhang J.: The obstacle problem for quasilinear stochastic PDEs: Analytical approach. The Annals of Probability, 42, 865--905 (2014).