Lewy–Stampacchia’s inequality for a stochastic T-monotone obstacle problem

The aim of this work is to study a stochastic obstacle problem governed by a T-monotone operator, a random force and a multiplicative stochastic reaction in the frame of Sobolev spaces. After proving a result of existence and uniqueness of the variational solution, by using an ad hoc perturbation of the stochastic reaction and a penalization of the constraint, we prove Lewy–Stampacchia’s inequalities associated with the problem finally.