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Abstract The article focuses on the qualitative analysis of the following stochastic variational inequality d u ( t ) + A ( t , u ( t ) ) d… Click to show full abstract
Abstract The article focuses on the qualitative analysis of the following stochastic variational inequality d u ( t ) + A ( t , u ( t ) ) d t + ∂ I K ( t ) ( u ( t ) ) d t ∋ g ( t , u ( t ) ) d W ( t ) , considered in a Gelfand–Lions triple space setup V ⊂ H ⊂ V ⋆ . We study the existence and uniqueness of a strong solution under the assumption of Holder continuity for the diffusion coefficient of our obstacle problem. Imposing some weaker assumptions on the barriers, we provide the existence of an weak variational solution for the multivalued problem. Moreover, the asymptotic behavior of the solution and a maximum principle are provided.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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