Suboptimal control of a semilinear elliptic equation with a phase constraint and a boundary control (Q5951225)

The paper considers a boundary control problem governed by the third boundary value problem for a semilinear elliptic equation with additional state constraints of the type \(y\in M+ q\subset C(Q)\), where \(Q\) is a compact subset of the reference domain \(\Omega\), \(q\) is a parameter and \(M\) is a convex closed set with nonempty interior. Necessary conditions which must satisfy approximating (with respect to the state constraints) minimizing sequences are obtained, and continuity properties of the value function of the problem with respect to the parameter \(q\) are investigated.