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.

中文翻译：

---

路易–斯坦帕基亚不等式对随机T-单调障碍问题的影响

这项工作的目的是研究在Sobolev空间框架中由T单调算子，随机力和乘法随机反应控制的随机障碍问题。在证明了变分解的存在性和唯一性之后，通过使用随机反应的临时扰动和约束的惩罚，我们最终证明了与问题相关的路易–斯坦帕基亚不等式。