抄録
In this paper, we study an optimal control problem with the state equation being a second order semilinear elliptic partial differential equation containing a distributed control. The control domain is not necessarily convex. The cost functional, which is to be minimized, is the essential supremum over the domain Ω of some function of the state and the control. Our main result is the Pontryagin type necessary conditions for the optimal control. Ekeland variational principle and the spike variation technique are used in proving our result.
