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Second-order optimality conditions for semilinear elliptic control problems with constraints on the gradient of the state

Casas E., Fernandez J., Mateos M.

Control and Cybernetics

1999

Vol. 28, no 3

463-479

The aim of this paper is to state the second order necessary and sufficient optimality conditions for distributed control problems governed by the Neumann problem associated to a semilinear elliptic partial differential equation. Bound constraints ou control are considered, as well as equality and inequality constraints of integral type on the gradient of the state.