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.

Automated summary

This work investigates a stochastic obstacle problem governed by a T-monotone operator, random force, and a multiplicative stochastic reaction in Sobolev spaces. It establishes the existence and uniqueness of the variational solution, and proves Lewy-Stampacchia's inequalities associated with the problem by perturbing the stochastic reaction and penalizing the constraint.