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Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. (English) Zbl 1037.49024

The authors present first and second order optimality conditions for optimal control problems of a semilinear equation of elliptic type, with Neumann boundary conditions and a distributed control. There are also bound control constraints as well as a finite number of abstract constraints on the state. They prove the equivalence of Lagrangian and Hamiltonian formulations.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
35J60 Nonlinear elliptic equations
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