4.3 Article

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

Publisher

SPRINGER
DOI: 10.1007/s40072-021-00194-x

Keywords

Stochastic PDEs; Obstacle problem; Wiener process; Lewy– Stampacchia’ s inequality

Funding

  1. IFCAM: Indo-French Center in Applied Mathematics [UMI CNRS 3494]

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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.
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.

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