Dealing with Integral State Constraints in BoundaryControl Problems of Quasilinear Elliptic Equations

This paper deals with state-constrained optimal control problems governed by a quasilinear elliptic equation. These constraints are given in an integral form and depend on the state and its gradient. Equality and inequality constraints are simultaneously considered. Existence of a solution is investigated and some optimality conditions are obtained with the aid of Ekeland's variational principle.