Affognon, Steeven BelvinosNgare, PhilipDegla, Guy2022-04-222022-04-222019-08-17Affognon,S.B., Ngare, P., Degla, G. (2019). Optimal Control Governed by Stochastic Elliptic Equations with Regular States. pg. 733-741. https://doi.org/10.12988/ams.2019.9690http://hdl.handle.net/123456789/1424Optimal control problems are currently among major research topics in applied mathematics, science engineering [1,2] and some related branches.This study deals with an optimal control problem subject to a stochastic elliptic equation with Dirichlet boundary condition and in which the state process is regular on a stochastic Hilbert space. We prove the existence and uniqueness of the optimal control and provide furthermore necessary and sufficient optimality conditions. The optimal solution is obtained in the case where there is no constraint. Our method is based on variational theory of elliptic boundary problems in Hilbert spacesenOptimal controlStochastic elliptic equationsStochastic Hilbert spaceStochastic fractional Sobolev spaceVariational formulationArticle