We  analyze an optimal control problem for a fractional semilinear PDE ; control constraints are also considered. We adopt the integral definition of the fractional Laplacian and establish the well-posedness of a fractional semilinear PDE; we also analyze suitable finite element discretizations. We thus derive the existence of optimal solutions and first and second order optimality conditions for our optimal control problem; regularity properties are also studied . We devise a fully discrete scheme that approximates the control variable with piecewise constant functions; the state and adjoint equations are discretized via piecewise linear finite elements. We analyze convergence properties of discretizations and obtain a priori error estimates.
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE) ; control constraints are also considered. We establish the well-posedness of fractional semilinear elliptic PDEs and analyze regularity properties and suitable finite element discretizations. Within the setting of our optimal control problem, we derive the existence of optimal solutions as well as first and second order optimality conditions ; regularity estimates for the optimal variables are also analyzed . We devise a fully discrete scheme that approximates the control variable with piecewise constant functions; the state and adjoint equations are discretized with continuous piecewise linear finite elements. We analyze convergence properties of discretizations and derive a priori error estimates.
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for our optimal control problem; regularity properties are also studied
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