Optimal control for cooperative systems involving fractional Laplace operators

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Abstract In this work, the elliptic $2\times 2$ 2 × 2 cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced.

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