Second-order necessary optimality conditions for some state-constrained control problems of semilinear elliptic equations (Q1283974)

The authors study second order necessary optimality conditions for a class of elliptic boundary control problems with pointwise constraints on the control, and either integral constraints on the state, or a finite number of pointwise constraints on the state. They give a precise characterization of the control directions which must satisfy second order optimality conditions. It is a continuation of a previous work by the authors and \textit{A. Unger} [J. Anal. Anwend. 15, No. 3, 687-707 (1996; Zbl 0879.49020)].